LMFDB - Embedded newform 368.2.i.b.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(91,368)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("368.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	368.91
Dual form			368.2.i.b.275.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33867 - 0.456028i) q^{2} +(0.860099 + 0.860099i) q^{3} +(1.58408 + 1.22094i) q^{4} +(0.0592628 - 0.0592628i) q^{5} +(-0.759160 - 1.54362i) q^{6} +2.65917i q^{7} +(-1.56377 - 2.35682i) q^{8} -1.52046i q^{9} +(-0.106359 + 0.0523078i) q^{10} +(3.23118 + 3.23118i) q^{11} +(0.312330 + 2.41260i) q^{12} +(1.32495 - 1.32495i) q^{13} +(1.21266 - 3.55975i) q^{14} +0.101944 q^{15} +(1.01859 + 3.86813i) q^{16} +1.27002i q^{17} +(-0.693372 + 2.03539i) q^{18} +(-4.69664 + 4.69664i) q^{19} +(0.166233 - 0.0215203i) q^{20} +(-2.28715 + 2.28715i) q^{21} +(-2.85197 - 5.79899i) q^{22} +(2.50175 - 4.09161i) q^{23} +(0.682105 - 3.37210i) q^{24} +4.99298i q^{25} +(-2.37788 + 1.16946i) q^{26} +(3.88804 - 3.88804i) q^{27} +(-3.24670 + 4.21233i) q^{28} +(-1.21823 + 1.21823i) q^{29} +(-0.136469 - 0.0464892i) q^{30} +2.31556i q^{31} +(0.400417 - 5.64266i) q^{32} +5.55826i q^{33} +(0.579165 - 1.70014i) q^{34} +(0.157590 + 0.157590i) q^{35} +(1.85639 - 2.40852i) q^{36} +(-1.54778 + 1.54778i) q^{37} +(8.42905 - 4.14545i) q^{38} +2.27918 q^{39} +(-0.232345 - 0.0469985i) q^{40} +2.46013i q^{41} +(4.10474 - 2.01873i) q^{42} +(8.21821 + 8.21821i) q^{43} +(1.17335 + 9.06351i) q^{44} +(-0.0901066 - 0.0901066i) q^{45} +(-5.21491 + 4.33645i) q^{46} -1.72980i q^{47} +(-2.45089 + 4.20307i) q^{48} -0.0711808 q^{49} +(2.27694 - 6.68395i) q^{50} +(-1.09234 + 1.09234i) q^{51} +(3.71651 - 0.481132i) q^{52} +(5.85076 - 5.85076i) q^{53} +(-6.97787 + 3.43175i) q^{54} +0.382977 q^{55} +(6.26719 - 4.15833i) q^{56} -8.07915 q^{57} +(2.18635 - 1.07526i) q^{58} +(10.2226 - 10.2226i) q^{59} +(0.161487 + 0.124468i) q^{60} +(-9.18423 - 9.18423i) q^{61} +(1.05596 - 3.09978i) q^{62} +4.04316 q^{63} +(-3.10924 + 7.37107i) q^{64} -0.157040i q^{65} +(2.53473 - 7.44068i) q^{66} +(0.241049 - 0.241049i) q^{67} +(-1.55062 + 2.01181i) q^{68} +(5.67094 - 1.36744i) q^{69} +(-0.139095 - 0.282826i) q^{70} -15.0134 q^{71} +(-3.58345 + 2.37765i) q^{72} -2.20672i q^{73} +(2.77781 - 1.36614i) q^{74} +(-4.29446 + 4.29446i) q^{75} +(-13.1742 + 1.70550i) q^{76} +(-8.59224 + 8.59224i) q^{77} +(-3.05107 - 1.03937i) q^{78} -6.90459 q^{79} +(0.289601 + 0.168872i) q^{80} +2.12683 q^{81} +(1.12189 - 3.29330i) q^{82} +(6.96262 - 6.96262i) q^{83} +(-6.41550 + 0.830539i) q^{84} +(0.0752648 + 0.0752648i) q^{85} +(-7.25373 - 14.7492i) q^{86} -2.09559 q^{87} +(2.56250 - 12.6681i) q^{88} -14.2609 q^{89} +(0.0795318 + 0.161714i) q^{90} +(3.52326 + 3.52326i) q^{91} +(8.95858 - 3.42693i) q^{92} +(-1.99162 + 1.99162i) q^{93} +(-0.788838 + 2.31563i) q^{94} +0.556672i q^{95} +(5.19765 - 4.50885i) q^{96} -7.99512i q^{97} +(0.0952876 + 0.0324605i) q^{98} +(4.91287 - 4.91287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.33867	−	0.456028i	−0.946583	−	0.322461i
$2$	−1.33867	−	0.456028i	−0.946583	−	0.322461i
$3$	0.860099	+	0.860099i	0.496579	+	0.496579i	0.910371	−	0.413793i	$-0.135796\pi$
$3$	0.860099	+	0.860099i	0.496579	+	0.496579i	−0.413793	+	0.910371i	$0.635796\pi$
$4$	1.58408	+	1.22094i	0.792038	+	0.610472i
$5$	0.0592628	−	0.0592628i	0.0265031	−	0.0265031i	−0.693731	−	0.720234i	$-0.744034\pi$
$5$	0.0592628	−	0.0592628i	0.0265031	−	0.0265031i	0.720234	+	0.693731i	$0.244034\pi$
$6$	−0.759160	−	1.54362i	−0.309926	−	0.630180i
$7$			2.65917i			1.00507i	0.864556	+	0.502536i	$0.167599\pi$
$7$			2.65917i			1.00507i	−0.864556	+	0.502536i	$0.832401\pi$
$8$	−1.56377	−	2.35682i	−0.552876	−	0.833263i
$9$		−	1.52046i		−	0.506819i
$10$	−0.106359	+	0.0523078i	−0.0336336	+	0.0165412i
$11$	3.23118	+	3.23118i	0.974236	+	0.974236i	0.999676	−	0.0254403i	$-0.00809877\pi$
$11$	3.23118	+	3.23118i	0.974236	+	0.974236i	−0.0254403	+	0.999676i	$0.508099\pi$
$12$	0.312330	+	2.41260i	0.0901620	+	0.696456i
$13$	1.32495	−	1.32495i	0.367475	−	0.367475i	−0.499081	−	0.866555i	$-0.666329\pi$
$13$	1.32495	−	1.32495i	0.367475	−	0.367475i	0.866555	+	0.499081i	$0.166329\pi$
$14$	1.21266	−	3.55975i	0.324096	−	0.951383i
$15$	0.101944			0.0263218
$16$	1.01859	+	3.86813i	0.254649	+	0.967034i
$17$			1.27002i			0.308025i	0.988069	+	0.154012i	$0.0492196\pi$
$17$			1.27002i			0.308025i	−0.988069	+	0.154012i	$0.950780\pi$
$18$	−0.693372	+	2.03539i	−0.163429	+	0.479747i
$19$	−4.69664	+	4.69664i	−1.07748	+	1.07748i	−0.0807484	+	0.996735i	$0.525731\pi$
$19$	−4.69664	+	4.69664i	−1.07748	+	1.07748i	−0.996735	+	0.0807484i	$0.974269\pi$
$20$	0.166233	−	0.0215203i	0.0371709	−	0.00481208i
$21$	−2.28715	+	2.28715i	−0.499097	+	0.499097i
$22$	−2.85197	−	5.79899i	−0.608042	−	1.23635i
$23$	2.50175	−	4.09161i	0.521651	−	0.853159i
$23$	2.50175	−	4.09161i	0.521651	−	0.853159i
$24$	0.682105	−	3.37210i	0.139234	−	0.688327i
$25$			4.99298i			0.998595i
$26$	−2.37788	+	1.16946i	−0.466342	+	0.229349i
$27$	3.88804	−	3.88804i	0.748254	−	0.748254i
$28$	−3.24670	+	4.21233i	−0.613568	+	0.796055i
$29$	−1.21823	+	1.21823i	−0.226219	+	0.226219i	−0.811111	−	0.584892i	$-0.801137\pi$
$29$	−1.21823	+	1.21823i	−0.226219	+	0.226219i	0.584892	+	0.811111i	$0.301137\pi$
$30$	−0.136469	−	0.0464892i	−0.0249157	−	0.00848774i
$31$			2.31556i			0.415888i	0.978141	+	0.207944i	$0.0666771\pi$
$31$			2.31556i			0.415888i	−0.978141	+	0.207944i	$0.933323\pi$
$32$	0.400417	−	5.64266i	0.0707844	−	0.997492i
$33$			5.55826i			0.967570i
$34$	0.579165	−	1.70014i	0.0993259	−	0.291571i
$35$	0.157590	+	0.157590i	0.0266375	+	0.0266375i
$36$	1.85639	−	2.40852i	0.309399	−	0.401420i
$37$	−1.54778	+	1.54778i	−0.254454	+	0.254454i	−0.822794	−	0.568340i	$-0.807586\pi$
$37$	−1.54778	+	1.54778i	−0.254454	+	0.254454i	0.568340	+	0.822794i	$0.307586\pi$
$38$	8.42905	−	4.14545i	1.36737	−	0.672481i
$39$	2.27918			0.364960
$40$	−0.232345	−	0.0469985i	−0.0367370	−	0.00743112i
$41$			2.46013i			0.384208i	0.981375	+	0.192104i	$0.0615310\pi$
$41$			2.46013i			0.384208i	−0.981375	+	0.192104i	$0.938469\pi$
$42$	4.10474	−	2.01873i	0.633376	−	0.311497i
$43$	8.21821	+	8.21821i	1.25326	+	1.25326i	0.954248	+	0.299017i	$0.0966588\pi$
$43$	8.21821	+	8.21821i	1.25326	+	1.25326i	0.299017	+	0.954248i	$0.403341\pi$
$44$	1.17335	+	9.06351i	0.176889	+	1.36638i
$45$	−0.0901066	−	0.0901066i	−0.0134323	−	0.0134323i
$46$	−5.21491	+	4.33645i	−0.768896	+	0.639374i
$47$		−	1.72980i		−	0.252317i	−0.992010	−	0.126159i	$-0.959735\pi$
$47$		−	1.72980i		−	0.252317i	0.992010	−	0.126159i	$-0.0402648\pi$
$48$	−2.45089	+	4.20307i	−0.353755	+	0.606661i
$49$	−0.0711808			−0.0101687
$50$	2.27694	−	6.68395i	0.322008	−	0.945253i
$51$	−1.09234	+	1.09234i	−0.152959	+	0.152959i
$52$	3.71651	−	0.481132i	0.515387	−	0.0667211i
$53$	5.85076	−	5.85076i	0.803663	−	0.803663i	−0.180003	−	0.983666i	$-0.557611\pi$
$53$	5.85076	−	5.85076i	0.803663	−	0.803663i	0.983666	+	0.180003i	$0.0576106\pi$
$54$	−6.97787	+	3.43175i	−0.949567	+	0.467002i
$55$	0.382977			0.0516406
$56$	6.26719	−	4.15833i	0.837489	−	0.555680i
$57$	−8.07915			−1.07011
$58$	2.18635	−	1.07526i	0.287082	−	0.141188i
$59$	10.2226	−	10.2226i	1.33088	−	1.33088i	0.426287	−	0.904588i	$-0.359821\pi$
$59$	10.2226	−	10.2226i	1.33088	−	1.33088i	0.904588	−	0.426287i	$-0.140179\pi$
$60$	0.161487	+	0.124468i	0.0208478	+	0.0160687i
$61$	−9.18423	−	9.18423i	−1.17592	−	1.17592i	−0.980774	−	0.195146i	$-0.937482\pi$
$61$	−9.18423	−	9.18423i	−1.17592	−	1.17592i	−0.195146	−	0.980774i	$-0.562518\pi$
$62$	1.05596	−	3.09978i	0.134107	−	0.393672i
$63$	4.04316			0.509390
$64$	−3.10924	+	7.37107i	−0.388655	+	0.921383i
$65$		−	0.157040i		−	0.0194785i
$66$	2.53473	−	7.44068i	0.312003	−	0.915885i
$67$	0.241049	−	0.241049i	0.0294489	−	0.0294489i	−0.692229	−	0.721678i	$-0.743371\pi$
$67$	0.241049	−	0.241049i	0.0294489	−	0.0294489i	0.721678	+	0.692229i	$0.243371\pi$
$68$	−1.55062	+	2.01181i	−0.188040	+	0.243967i
$69$	5.67094	−	1.36744i	0.682701	−	0.164620i
$70$	−0.139095	−	0.282826i	−0.0166251	−	0.0338042i
$71$	−15.0134			−1.78176			−0.890879	−	0.454241i	$-0.849911\pi$
$71$	−15.0134			−1.78176			−0.890879	+	0.454241i	$0.849911\pi$
$72$	−3.58345	+	2.37765i	−0.422314	+	0.280208i
$73$		−	2.20672i		−	0.258277i	−0.991627	−	0.129139i	$-0.958779\pi$
$73$		−	2.20672i		−	0.258277i	0.991627	−	0.129139i	$-0.0412212\pi$
$74$	2.77781	−	1.36614i	0.322913	−	0.158810i
$75$	−4.29446	+	4.29446i	−0.495881	+	0.495881i
$76$	−13.1742	+	1.70550i	−1.51118	+	0.195635i
$77$	−8.59224	+	8.59224i	−0.979177	+	0.979177i
$78$	−3.05107	−	1.03937i	−0.345465	−	0.117685i
$79$	−6.90459			−0.776827			−0.388414	−	0.921485i	$-0.626977\pi$
$79$	−6.90459			−0.776827			−0.388414	+	0.921485i	$0.626977\pi$
$80$	0.289601	+	0.168872i	0.0323784	+	0.0188804i
$81$	2.12683			0.236315
$82$	1.12189	−	3.29330i	0.123892	−	0.363684i
$83$	6.96262	−	6.96262i	0.764247	−	0.764247i	−0.212840	−	0.977087i	$-0.568271\pi$
$83$	6.96262	−	6.96262i	0.764247	−	0.764247i	0.977087	+	0.212840i	$0.0682714\pi$
$84$	−6.41550	+	0.830539i	−0.699988	+	0.0906192i
$85$	0.0752648	+	0.0752648i	0.00816362	+	0.00816362i
$86$	−7.25373	−	14.7492i	−0.782190	−	1.59045i
$87$	−2.09559			−0.224671
$88$	2.56250	−	12.6681i	0.273163	−	1.35043i
$89$	−14.2609			−1.51166			−0.755828	−	0.654771i	$-0.772765\pi$
$89$	−14.2609			−1.51166			−0.755828	+	0.654771i	$0.772765\pi$
$90$	0.0795318	+	0.161714i	0.00838339	+	0.0170462i
$91$	3.52326	+	3.52326i	0.369338	+	0.369338i
$92$	8.95858	−	3.42693i	0.933997	−	0.357282i
$93$	−1.99162	+	1.99162i	−0.206521	+	0.206521i
$94$	−0.788838	+	2.31563i	−0.0813625	+	0.238839i
$95$			0.556672i			0.0571133i
$96$	5.19765	−	4.50885i	0.530483	−	0.460183i
$97$		−	7.99512i		−	0.811781i	−0.913922	−	0.405891i	$-0.866961\pi$
$97$		−	7.99512i		−	0.811781i	0.913922	−	0.405891i	$-0.133039\pi$
$98$	0.0952876	+	0.0324605i	0.00962550	+	0.00327900i
$99$	4.91287	−	4.91287i	0.493762	−	0.493762i
$100$	−6.09614	+	7.90925i	−0.609614	+	0.790925i
$101$	−3.64570	−	3.64570i	−0.362760	−	0.362760i	0.502068	−	0.864828i	$-0.332573\pi$
$101$	−3.64570	−	3.64570i	−0.362760	−	0.362760i	−0.864828	+	0.502068i	$0.832573\pi$
$102$	1.96043	−	0.964147i	0.194111	−	0.0954648i
$103$		−	13.3253i		−	1.31298i	−0.754333	−	0.656492i	$-0.772039\pi$
$103$		−	13.3253i		−	1.31298i	0.754333	−	0.656492i	$-0.227961\pi$
$104$	−5.19459	−	1.05076i	−0.509371	−	0.103035i
$105$			0.271086i			0.0264553i
$106$	−10.5003	+	5.16412i	−1.01988	+	0.501584i
$107$	7.02903	+	7.02903i	0.679522	+	0.679522i	0.959892	−	0.280370i	$-0.0904570\pi$
$107$	7.02903	+	7.02903i	0.679522	+	0.679522i	−0.280370	+	0.959892i	$0.590457\pi$
$108$	10.9060	−	1.41188i	1.04943	−	0.135858i
$109$	−3.12657	−	3.12657i	−0.299471	−	0.299471i	0.541335	−	0.840807i	$-0.317919\pi$
$109$	−3.12657	−	3.12657i	−0.299471	−	0.299471i	−0.840807	+	0.541335i	$0.817919\pi$
$110$	−0.512680	−	0.174648i	−0.0488821	−	0.0166521i
$111$	−2.66250			−0.252713
$112$	−10.2860	+	2.70862i	−0.971938	+	0.255940i
$113$		−	8.66950i		−	0.815558i	−0.913081	−	0.407779i	$-0.866303\pi$
$113$		−	8.66950i		−	0.815558i	0.913081	−	0.407779i	$-0.133697\pi$
$114$	10.8153	+	3.68432i	1.01295	+	0.345069i
$115$	−0.0942195	−	0.390741i	−0.00878601	−	0.0364367i
$116$	−3.41715	+	0.442378i	−0.317274	+	0.0410738i
$117$	−2.01453	−	2.01453i	−0.186243	−	0.186243i
$118$	−18.3466	+	9.02293i	−1.68894	+	0.830628i
$119$	−3.37719			−0.309587
$120$	−0.159417	−	0.240263i	−0.0145527	−	0.0219330i
$121$			9.88099i			0.898272i
$122$	8.10638	+	16.4829i	0.733918	+	1.49229i
$123$	−2.11596	+	2.11596i	−0.190789	+	0.190789i
$124$	−2.82717	+	3.66803i	−0.253888	+	0.329399i
$125$	0.592211	+	0.592211i	0.0529690	+	0.0529690i
$126$	−5.41245	−	1.84379i	−0.482180	−	0.164258i
$127$		−	5.22135i		−	0.463320i	−0.972797	−	0.231660i	$-0.925584\pi$
$127$		−	5.22135i		−	0.463320i	0.972797	−	0.231660i	$-0.0744157\pi$
$128$	7.52367	−	8.44952i	0.665004	−	0.746839i
$129$			14.1370i			1.24469i
$130$	−0.0716148	+	0.210225i	−0.00628104	+	0.0184380i
$131$	3.33453	+	3.33453i	0.291339	+	0.291339i	0.837609	−	0.546270i	$-0.183953\pi$
$131$	3.33453	+	3.33453i	0.291339	+	0.291339i	−0.546270	+	0.837609i	$0.683953\pi$
$132$	−6.78633	+	8.80471i	−0.590674	+	0.766352i
$133$	−12.4892	−	12.4892i	−1.08295	−	1.08295i
$134$	−0.432611	+	0.212760i	−0.0373719	+	0.0183797i
$135$		−	0.460832i		−	0.0396621i
$136$	2.99321	−	1.98602i	0.256666	−	0.170300i
$137$	−7.42500			−0.634361			−0.317180	−	0.948365i	$-0.602736\pi$
$137$	−7.42500			−0.634361			−0.317180	+	0.948365i	$0.602736\pi$
$138$	−8.21511	−	0.755563i	−0.699317	−	0.0643178i
$139$	6.66197	−	6.66197i	0.565061	−	0.565061i	−0.365680	−	0.930741i	$-0.619164\pi$
$139$	6.66197	−	6.66197i	0.565061	−	0.565061i	0.930741	+	0.365680i	$0.119164\pi$
$140$	0.0572260	+	0.442042i	0.00483648	+	0.0373594i
$141$	1.48780	−	1.48780i	0.125295	−	0.125295i
$142$	20.0979	+	6.84652i	1.68658	+	0.574547i
$143$	8.56229			0.716014
$144$	5.88134	−	1.54873i	0.490111	−	0.129061i
$145$			0.144391i			0.0119910i
$146$	−1.00633	+	2.95407i	−0.0832843	+	0.244481i
$147$	−0.0612226	−	0.0612226i	−0.00504955	−	0.00504955i
$148$	−4.34156	+	0.562051i	−0.356874	+	0.0462003i
$149$	6.57835	−	6.57835i	0.538920	−	0.538920i	−0.384292	−	0.923212i	$-0.625554\pi$
$149$	6.57835	−	6.57835i	0.538920	−	0.538920i	0.923212	+	0.384292i	$0.125554\pi$
$150$	7.70725	−	3.79047i	0.629295	−	0.309490i
$151$	15.6057			1.26997			0.634986	−	0.772524i	$-0.281006\pi$
$151$	15.6057			1.26997			0.634986	+	0.772524i	$0.281006\pi$
$152$	18.4136	+	3.72469i	1.49354	+	0.302112i
$153$	1.93101			0.156113
$154$	15.4205	−	7.58387i	1.24262	−	0.611126i
$155$	0.137227	+	0.137227i	0.0110223	+	0.0110223i
$156$	3.61039	+	2.78274i	0.289062	+	0.222798i
$157$	6.05567	+	6.05567i	0.483295	+	0.483295i	0.906182	−	0.422887i	$-0.138983\pi$
$157$	6.05567	+	6.05567i	0.483295	+	0.483295i	−0.422887	+	0.906182i	$0.638983\pi$
$158$	9.24297	+	3.14869i	0.735331	+	0.250496i
$159$	10.0645			0.798164
$160$	−0.310670	−	0.358130i	−0.0245606	−	0.0283126i
$161$	10.8803	+	6.65257i	0.857486	+	0.524296i
$162$	−2.84713	−	0.969896i	−0.223692	−	0.0762022i
$163$	−10.7888	−	10.7888i	−0.845040	−	0.845040i	0.144469	−	0.989509i	$-0.453853\pi$
$163$	−10.7888	−	10.7888i	−0.845040	−	0.845040i	−0.989509	+	0.144469i	$0.953853\pi$
$164$	−3.00368	+	3.89703i	−0.234548	+	0.304307i
$165$	0.329398	+	0.329398i	0.0256436	+	0.0256436i
$166$	−12.4958	+	6.14550i	−0.969862	+	0.476983i
$167$	−6.67959			−0.516882			−0.258441	−	0.966027i	$-0.583209\pi$
$167$	−6.67959			−0.516882			−0.258441	+	0.966027i	$0.583209\pi$
$168$	8.96699	+	1.81383i	0.691818	+	0.139940i
$169$			9.48902i			0.729925i
$170$	−0.0664319	−	0.135078i	−0.00509509	−	0.0103600i
$171$	7.14104	+	7.14104i	0.546089	+	0.546089i
$172$	2.98430	+	23.0522i	0.227551	+	1.75772i
$173$	9.10911	−	9.10911i	0.692553	−	0.692553i	−0.270240	−	0.962793i	$-0.587103\pi$
$173$	9.10911	−	9.10911i	0.692553	−	0.692553i	0.962793	+	0.270240i	$0.0871030\pi$
$174$	2.80531	+	0.955650i	0.212670	+	0.0724476i
$175$	−13.2772			−1.00366
$176$	−9.20736	+	15.7899i	−0.694031	+	1.19021i
$177$	17.5850			1.32177
$178$	19.0907	+	6.50339i	1.43091	+	0.487449i
$179$	0.0909711	+	0.0909711i	0.00679950	+	0.00679950i	0.710498	−	0.703699i	$-0.248470\pi$
$179$	0.0909711	+	0.0909711i	0.00679950	+	0.00679950i	−0.703699	+	0.710498i	$0.748470\pi$
$180$	−0.0327206	−	0.252751i	−0.00243885	−	0.0188389i
$181$	11.3170	−	11.3170i	0.841187	−	0.841187i	−0.147826	−	0.989013i	$-0.547228\pi$
$181$	11.3170	−	11.3170i	0.841187	−	0.841187i	0.989013	+	0.147826i	$0.0472276\pi$
$182$	−3.10978	−	6.32320i	−0.230512	−	0.468707i
$183$		−	15.7987i		−	1.16787i
$184$	−13.5554	+	0.502156i	−0.999315	+	0.0370194i
$185$			0.183452i			0.0134877i
$186$	3.57435	−	1.75788i	0.262084	−	0.128894i
$187$	−4.10365	+	4.10365i	−0.300089	+	0.300089i
$188$	2.11199	−	2.74014i	0.154033	−	0.199845i
$189$	10.3390	+	10.3390i	0.752049	+	0.752049i
$190$	0.253858	−	0.745200i	0.0184168	−	0.0540625i
$191$	−15.7543			−1.13994			−0.569972	−	0.821664i	$-0.693046\pi$
$191$	−15.7543			−1.13994			−0.569972	+	0.821664i	$0.693046\pi$
$192$	−9.01411	+	3.66559i	−0.650537	+	0.264541i
$193$	−9.94979			−0.716202			−0.358101	−	0.933683i	$-0.616576\pi$
$193$	−9.94979			−0.716202			−0.358101	+	0.933683i	$0.616576\pi$
$194$	−3.64600	+	10.7028i	−0.261768	+	0.768418i
$195$	0.135070	−	0.135070i	0.00967258	−	0.00967258i
$196$	−0.112756	−	0.0869077i	−0.00805399	−	0.00620770i
$197$	12.0238	+	12.0238i	0.856661	+	0.856661i	0.990943	−	0.134282i	$-0.0428729\pi$
$197$	12.0238	+	12.0238i	0.856661	+	0.856661i	−0.134282	+	0.990943i	$0.542873\pi$
$198$	−8.81712	+	4.33630i	−0.626605	+	0.308168i
$199$			12.1254i			0.859544i	0.902937	+	0.429772i	$0.141406\pi$
$199$			12.1254i			0.859544i	−0.902937	+	0.429772i	$0.858594\pi$
$200$	11.7676	−	7.80787i	0.832093	−	0.552100i
$201$	0.414653			0.0292473
$202$	3.21785	+	6.54293i	0.226407	+	0.460359i
$203$	−3.23947	−	3.23947i	−0.227366	−	0.227366i
$204$	−3.06404	+	0.396665i	−0.214526	+	0.0277721i
$205$	0.145794	+	0.145794i	0.0101827	+	0.0101827i
$206$	−6.07673	+	17.8382i	−0.423386	+	1.24285i
$207$	−6.22112	−	3.80380i	−0.432398	−	0.264383i
$208$	6.47467	+	3.77550i	0.448937	+	0.261784i
$209$	−30.3513			−2.09945
$210$	0.123623	−	0.362894i	0.00853078	−	0.0250421i
$211$	8.84817	+	8.84817i	0.609133	+	0.609133i	0.942720	−	0.333586i	$-0.108259\pi$
$211$	8.84817	+	8.84817i	0.609133	+	0.609133i	−0.333586	+	0.942720i	$0.608259\pi$
$212$	16.4115	−	2.12460i	1.12715	−	0.145918i
$213$	−12.9130	−	12.9130i	−0.884783	−	0.884783i
$214$	−6.20412	−	12.6150i	−0.424105	−	0.862344i
$215$	0.974067			0.0664308
$216$	−15.2434	−	3.08343i	−1.03718	−	0.209801i
$217$	−6.15748			−0.417997
$218$	2.75964	+	5.61125i	0.186907	+	0.380042i
$219$	1.89800	−	1.89800i	0.128255	−	0.128255i
$220$	0.606664	+	0.467593i	0.0409013	+	0.0315251i
$221$	1.68271	+	1.68271i	0.113191	+	0.113191i
$222$	3.56420	+	1.21417i	0.239214	+	0.0814900i
$223$			8.33600i			0.558220i	0.960259	+	0.279110i	$0.0900394\pi$
$223$			8.33600i			0.558220i	−0.960259	+	0.279110i	$0.909961\pi$
$224$	15.0048	+	1.06478i	1.00255	+	0.0711434i
$225$	7.59161			0.506107
$226$	−3.95354	+	11.6056i	−0.262985	+	0.771993i
$227$	−4.72544	+	4.72544i	−0.313638	+	0.313638i	−0.846317	−	0.532679i	$-0.821185\pi$
$227$	−4.72544	+	4.72544i	−0.313638	+	0.313638i	0.532679	+	0.846317i	$0.321185\pi$
$228$	−12.7980	−	9.86419i	−0.847568	−	0.653272i
$229$	15.7355	−	15.7355i	1.03983	−	1.03983i	0.0406573	−	0.999173i	$-0.487055\pi$
$229$	15.7355	−	15.7355i	1.03983	−	1.03983i	0.999173	−	0.0406573i	$-0.0129452\pi$
$230$	−0.0520600	+	0.566040i	−0.00343273	+	0.0373235i
$231$	−14.7804			−0.972477
$232$	4.77617	+	0.966119i	0.313571	+	0.0634288i
$233$		−	5.06132i		−	0.331578i	−0.986161	−	0.165789i	$-0.946983\pi$
$233$		−	5.06132i		−	0.331578i	0.986161	−	0.165789i	$-0.0530171\pi$
$234$	1.77811	+	3.61547i	0.116239	+	0.236351i
$235$	−0.102513	−	0.102513i	−0.00668720	−	0.00668720i
$236$	28.6747	−	3.71218i	1.86657	−	0.241642i
$237$	−5.93863	−	5.93863i	−0.385756	−	0.385756i
$238$	4.52095	+	1.54010i	0.293050	+	0.0998297i
$239$			25.4452i			1.64591i	0.568105	+	0.822956i	$0.307677\pi$
$239$			25.4452i			1.64591i	−0.568105	+	0.822956i	$0.692323\pi$
$240$	0.103839	+	0.394332i	0.00670280	+	0.0254540i
$241$			7.67284i			0.494251i	0.968983	+	0.247126i	$0.0794860\pi$
$241$			7.67284i			0.494251i	−0.968983	+	0.247126i	$0.920514\pi$
$242$	4.50601	−	13.2274i	0.289657	−	0.850289i
$243$	−9.83484	−	9.83484i	−0.630905	−	0.630905i
$244$	−3.33509	−	25.7619i	−0.213508	−	1.64924i
$245$	−0.00421837	+	0.00421837i	−0.000269502	+	0.000269502i
$246$	3.79750	−	1.86763i	0.242120	−	0.119076i
$247$			12.4456i			0.791896i
$248$	5.45738	−	3.62101i	0.346544	−	0.229934i
$249$	11.9771			0.759017
$250$	−0.522711	−	1.06284i	−0.0330591	−	0.0672200i
$251$	−18.0092	−	18.0092i	−1.13673	−	1.13673i	−0.989033	−	0.147695i	$-0.952814\pi$
$251$	−18.0092	−	18.0092i	−1.13673	−	1.13673i	−0.147695	−	0.989033i	$-0.547186\pi$
$252$	6.40467	+	4.93646i	0.403456	+	0.310968i
$253$	21.3043	−	5.13712i	1.33939	−	0.322968i
$254$	−2.38108	+	6.98967i	−0.149403	+	0.438571i
$255$			0.129470i			0.00810776i
$256$	−13.9249	+	7.88012i	−0.870308	+	0.492508i
$257$	−11.5321			−0.719351			−0.359675	−	0.933077i	$-0.617113\pi$
$257$	−11.5321			−0.719351			−0.359675	+	0.933077i	$0.617113\pi$
$258$	6.44685	−	18.9247i	0.401363	−	1.17820i
$259$	−4.11582	−	4.11582i	−0.255745	−	0.255745i
$260$	0.191737	−	0.248764i	0.0118910	−	0.0154277i
$261$	1.85226	+	1.85226i	0.114652	+	0.114652i
$262$	−2.94320	−	5.98448i	−0.181831	−	0.369722i
$263$		−	25.8401i		−	1.59337i	−0.604396	−	0.796684i	$-0.706586\pi$
$263$		−	25.8401i		−	1.59337i	0.604396	−	0.796684i	$-0.293414\pi$
$264$	13.0999	−	8.69185i	0.806240	−	0.534946i
$265$		−	0.693464i		−	0.0425992i
$266$	11.0235	+	22.4143i	0.675891	+	1.37431i
$267$	−12.2658	−	12.2658i	−0.750656	−	0.750656i
$268$	0.676148	−	0.0875329i	0.0413023	−	0.00534692i
$269$	12.0864	−	12.0864i	0.736922	−	0.736922i	−0.235059	−	0.971981i	$-0.575528\pi$
$269$	12.0864	−	12.0864i	0.736922	−	0.736922i	0.971981	+	0.235059i	$0.0755284\pi$
$270$	−0.210153	+	0.616903i	−0.0127895	+	0.0375435i
$271$			19.6896i			1.19606i	0.801474	+	0.598030i	$0.204050\pi$
$271$			19.6896i			1.19606i	−0.801474	+	0.598030i	$0.795950\pi$
$272$	−4.91260	+	1.29363i	−0.297870	+	0.0784381i
$273$			6.06071i			0.366811i
$274$	9.93963	+	3.38601i	0.600475	+	0.204556i
$275$	−16.1332	+	16.1332i	−0.972867	+	0.972867i
$276$	10.6528	+	4.75777i	0.641221	+	0.286384i
$277$	−8.60109	−	8.60109i	−0.516789	−	0.516789i	0.399809	−	0.916598i	$-0.369076\pi$
$277$	−8.60109	−	8.60109i	−0.516789	−	0.516789i	−0.916598	+	0.399809i	$0.869076\pi$
$278$	−11.9562	+	5.88013i	−0.717087	+	0.352667i
$279$	3.52072			0.210780
$280$	0.124977	−	0.617846i	0.00746881	−	0.0369233i
$281$	−28.6536			−1.70933			−0.854665	−	0.519181i	$-0.826237\pi$
$281$	−28.6536			−1.70933			−0.854665	+	0.519181i	$0.826237\pi$
$282$	−2.67015	+	1.31319i	−0.159005	+	0.0781996i
$283$	4.00191	+	4.00191i	0.237889	+	0.237889i	0.815976	−	0.578086i	$-0.196200\pi$
$283$	4.00191	+	4.00191i	0.237889	+	0.237889i	−0.578086	+	0.815976i	$0.696200\pi$
$284$	−23.7823	−	18.3305i	−1.41122	−	1.08771i
$285$	−0.478793	+	0.478793i	−0.0283612	+	0.0283612i
$286$	−11.4621	−	3.90465i	−0.677767	−	0.230887i
$287$	−6.54190			−0.386156
$288$	−8.57944	−	0.608817i	−0.505548	−	0.0358749i
$289$	15.3871			0.905121
$290$	0.0658464	−	0.193292i	0.00386663	−	0.0113505i
$291$	6.87660	−	6.87660i	0.403113	−	0.403113i
$292$	2.69428	−	3.49562i	0.157671	−	0.204565i
$293$	−9.94696	+	9.94696i	−0.581107	+	0.581107i	−0.935208	−	0.354100i	$-0.884787\pi$
$293$	−9.94696	+	9.94696i	−0.581107	+	0.581107i	0.354100	+	0.935208i	$0.384787\pi$
$294$	0.0540376	+	0.109876i	0.00315154	+	0.00640810i
$295$		−	1.21164i		−	0.0705447i
$296$	6.06823	+	1.22748i	0.352709	+	0.0713456i
$297$	25.1259			1.45795
$298$	−11.8062	+	5.80633i	−0.683912	+	0.336352i
$299$	−2.10648	−	8.73586i	−0.121821	−	0.505208i
$300$	−12.0460	+	1.55946i	−0.695478	+	0.0900353i
$301$	−21.8536	+	21.8536i	−1.25962	+	1.25962i
$302$	−20.8909	−	7.11663i	−1.20213	−	0.409516i
$303$		−	6.27132i		−	0.360278i
$304$	−22.9512	−	13.3833i	−1.31634	−	0.767583i
$305$	−1.08857			−0.0623311
$306$	−2.58499	−	0.880596i	−0.147774	−	0.0503403i
$307$	10.7455	+	10.7455i	0.613280	+	0.613280i	0.943799	−	0.330519i	$-0.107224\pi$
$307$	10.7455	+	10.7455i	0.613280	+	0.613280i	−0.330519	+	0.943799i	$0.607224\pi$
$308$	−24.1014	+	3.12012i	−1.37331	+	0.177786i
$309$	11.4611	−	11.4611i	0.652000	−	0.652000i
$310$	−0.121122	−	0.246281i	−0.00687927	−	0.0139878i
$311$	14.1242			0.800908			0.400454	−	0.916317i	$-0.368852\pi$
$311$	14.1242			0.800908			0.400454	+	0.916317i	$0.368852\pi$
$312$	−3.56411	−	5.37162i	−0.201778	−	0.304108i
$313$	24.3707			1.37751			0.688757	−	0.724992i	$-0.258157\pi$
$313$	24.3707			1.37751			0.688757	+	0.724992i	$0.258157\pi$
$314$	−5.34499	−	10.8681i	−0.301635	−	0.613323i
$315$	0.239609	−	0.239609i	0.0135004	−	0.0135004i
$316$	−10.9374	−	8.43011i	−0.615277	−	0.474231i
$317$	10.5047	−	10.5047i	0.590001	−	0.590001i	−0.347630	−	0.937632i	$-0.613014\pi$
$317$	10.5047	−	10.5047i	0.590001	−	0.590001i	0.937632	+	0.347630i	$0.113014\pi$
$318$	−13.4730	−	4.58968i	−0.755529	−	0.257377i
$319$	−7.87261			−0.440781
$320$	0.252567	+	0.621092i	0.0141190	+	0.0347201i
$321$			12.0913i			0.674873i
$322$	−11.5313	−	13.8673i	−0.642617	−	0.772795i
$323$	−5.96482	−	5.96482i	−0.331891	−	0.331891i
$324$	3.36907	+	2.59674i	0.187170	+	0.144263i
$325$	6.61544	+	6.61544i	0.366959	+	0.366959i
$326$	9.52260	+	19.3626i	0.527408	+	1.07239i
$327$		−	5.37833i		−	0.297422i
$328$	5.79809	−	3.84708i	0.320146	−	0.212419i
$329$	4.59983			0.253597
$330$	−0.290741	−	0.591170i	−0.0160047	−	0.0325429i
$331$	−8.83567	+	8.83567i	−0.485652	+	0.485652i	−0.906931	−	0.421279i	$-0.861581\pi$
$331$	−8.83567	+	8.83567i	−0.485652	+	0.485652i	0.421279	+	0.906931i	$0.361581\pi$
$332$	19.5303	−	2.52836i	1.07186	−	0.138762i
$333$	2.35334	+	2.35334i	0.128962	+	0.128962i
$334$	8.94177	+	3.04608i	0.489272	+	0.166674i
$335$		−	0.0285705i		−	0.00156097i
$336$	−11.1767	−	6.51732i	−0.609738	−	0.355549i
$337$		−	10.6494i		−	0.580110i	−0.957010	−	0.290055i	$-0.906326\pi$
$337$		−	10.6494i		−	0.580110i	0.957010	−	0.290055i	$-0.0936735\pi$
$338$	4.32726	−	12.7027i	0.235372	−	0.690934i
$339$	7.45663	−	7.45663i	0.404989	−	0.404989i
$340$	0.0273311	+	0.211119i	0.00148224	+	0.0114496i
$341$	−7.48199	+	7.48199i	−0.405173	+	0.405173i
$342$	−6.30298	−	12.8160i	−0.340826	−	0.693011i
$343$			18.4249i			0.994851i
$344$	6.51748	−	32.2203i	0.351399	−	1.73720i
$345$	0.255038	−	0.417114i	0.0137308	−	0.0224567i
$346$	−16.3481	+	8.04009i	−0.878880	+	0.432238i
$347$	−16.4276	+	16.4276i	−0.881879	+	0.881879i	−0.993725	−	0.111847i	$-0.964323\pi$
$347$	−16.4276	+	16.4276i	−0.881879	+	0.881879i	0.111847	+	0.993725i	$0.464323\pi$
$348$	−3.31958	−	2.55860i	−0.177948	−	0.137155i
$349$	−5.53040	+	5.53040i	−0.296036	+	0.296036i	−0.839459	−	0.543423i	$-0.817128\pi$
$349$	−5.53040	+	5.53040i	−0.296036	+	0.296036i	0.543423	+	0.839459i	$0.317128\pi$
$350$	17.7737	+	6.05477i	0.950047	+	0.323641i
$351$		−	10.3029i		−	0.549929i
$352$	19.5263	−	16.9386i	1.04075	−	0.902832i
$353$	32.2050			1.71410			0.857050	−	0.515233i	$-0.172295\pi$
$353$	32.2050			1.71410			0.857050	+	0.515233i	$0.172295\pi$
$354$	−23.5405	−	8.01925i	−1.25116	−	0.426218i
$355$	−0.889733	+	0.889733i	−0.0472221	+	0.0472221i
$356$	−22.5904	−	17.4118i	−1.19729	−	0.922823i
$357$	−2.90472	−	2.90472i	−0.153734	−	0.153734i
$358$	−0.0802949	−	0.163266i	−0.00424372	−	0.00862886i
$359$			13.6769i			0.721838i	0.932597	+	0.360919i	$0.117537\pi$
$359$			13.6769i			0.721838i	−0.932597	+	0.360919i	$0.882463\pi$
$360$	−0.0714593	+	0.353271i	−0.00376624	+	0.0186190i
$361$		−	25.1168i		−	1.32194i
$362$	−20.3106	+	9.98887i	−1.06750	+	0.525004i
$363$	−8.49863	+	8.49863i	−0.446063	+	0.446063i
$364$	1.27941	+	9.88282i	0.0670594	+	0.518001i
$365$	−0.130776	−	0.130776i	−0.00684515	−	0.00684515i
$366$	−7.20466	+	21.1492i	−0.376593	+	1.10549i
$367$	−18.4813			−0.964716			−0.482358	−	0.875974i	$-0.660220\pi$
$367$	−18.4813			−0.964716			−0.482358	+	0.875974i	$0.660220\pi$
$368$	18.3752	+	5.50941i	0.957871	+	0.287198i
$369$	3.74052			0.194724
$370$	0.0836593	−	0.245582i	0.00434924	−	0.0127672i
$371$	15.5582	+	15.5582i	0.807739	+	0.807739i
$372$	−5.58652	+	0.723221i	−0.289648	+	0.0374973i
$373$	−2.68817	+	2.68817i	−0.139188	+	0.139188i	−0.773268	−	0.634080i	$-0.781379\pi$
$373$	−2.68817	+	2.68817i	−0.139188	+	0.139188i	0.634080	+	0.773268i	$0.281379\pi$
$374$	7.36482	−	3.62206i	0.380826	−	0.187292i
$375$			1.01872i			0.0526065i
$376$	−4.07684	+	2.70501i	−0.210247	+	0.139500i
$377$			3.22818i			0.166260i
$378$	−9.12560	−	18.5553i	−0.469370	−	0.954383i
$379$	17.1581	+	17.1581i	0.881353	+	0.881353i	0.993672	−	0.112319i	$-0.0358279\pi$
$379$	17.1581	+	17.1581i	0.881353	+	0.881353i	−0.112319	+	0.993672i	$0.535828\pi$
$380$	−0.679665	+	0.881810i	−0.0348661	+	0.0452359i
$381$	4.49088	−	4.49088i	0.230075	−	0.230075i
$382$	21.0899	+	7.18442i	1.07905	+	0.367587i
$383$	9.20129			0.470164			0.235082	−	0.971976i	$-0.424464\pi$
$383$	9.20129			0.470164			0.235082	+	0.971976i	$0.424464\pi$
$384$	13.7385	−	0.796331i	0.701091	−	0.0406376i
$385$			1.01840i			0.0519025i
$386$	13.3195	+	4.53739i	0.677944	+	0.230947i
$387$	12.4954	−	12.4954i	0.635179	−	0.635179i
$388$	9.76159	−	12.6649i	0.495569	−	0.642962i
$389$	−19.1433	+	19.1433i	−0.970606	+	0.970606i	−0.999580	−	0.0289741i	$-0.990776\pi$
$389$	−19.1433	+	19.1433i	−0.970606	+	0.970606i	0.0289741	+	0.999580i	$0.490776\pi$
$390$	−0.242410	+	0.119219i	−0.0122749	+	0.00603687i
$391$	5.19642	+	3.17727i	0.262794	+	0.160681i
$392$	0.111310	+	0.167761i	0.00562203	+	0.00847319i
$393$			5.73606i			0.289346i
$394$	−10.6127	−	21.5791i	−0.534661	−	1.08714i
$395$	−0.409185	+	0.409185i	−0.0205883	+	0.0205883i
$396$	13.7807	−	1.78402i	0.692506	−	0.0896505i
$397$	4.43182	−	4.43182i	0.222426	−	0.222426i	−0.587093	−	0.809519i	$-0.699728\pi$
$397$	4.43182	−	4.43182i	0.222426	−	0.222426i	0.809519	+	0.587093i	$0.199728\pi$
$398$	5.52951	−	16.2319i	0.277169	−	0.813630i
$399$		−	21.4838i		−	1.07554i
$400$	−19.3135	+	5.08582i	−0.965675	+	0.254291i
$401$			9.14611i			0.456735i	0.973575	+	0.228367i	$0.0733388\pi$
$401$			9.14611i			0.456735i	−0.973575	+	0.228367i	$0.926661\pi$
$402$	−0.555083	−	0.189093i	−0.0276850	−	0.00943112i
$403$	3.06801	+	3.06801i	0.152828	+	0.152828i
$404$	−1.32387	−	10.2263i	−0.0658651	−	0.508775i
$405$	0.126042	−	0.126042i	0.00626308	−	0.00626308i
$406$	2.85929	+	5.81387i	0.141904	+	0.288538i
$407$	−10.0023			−0.495797
$408$	4.28263	+	0.866286i	0.212022	+	0.0428876i
$409$		−	38.6304i		−	1.91015i	−0.296365	−	0.955075i	$-0.595775\pi$
$409$		−	38.6304i		−	1.91015i	0.296365	−	0.955075i	$-0.404225\pi$
$410$	−0.128684	−	0.261656i	−0.00635525	−	0.0129223i
$411$	−6.38624	−	6.38624i	−0.315010	−	0.315010i
$412$	16.2695	−	21.1083i	0.801540	−	1.03993i
$413$	27.1837	+	27.1837i	1.33762	+	1.33762i
$414$	6.59338	+	7.92905i	0.324047	+	0.389691i
$415$		−	0.825248i		−	0.0405098i
$416$	−6.94571	−	8.00678i	−0.340542	−	0.392565i
$417$	11.4599			0.561194
$418$	40.6304	+	13.8411i	1.98730	+	0.676989i
$419$	−12.1063	+	12.1063i	−0.591429	+	0.591429i	−0.938017	−	0.346588i	$-0.887340\pi$
$419$	−12.1063	+	12.1063i	−0.591429	+	0.591429i	0.346588	+	0.938017i	$0.387340\pi$
$420$	−0.330980	+	0.429420i	−0.0161502	+	0.0209536i
$421$	−13.6001	+	13.6001i	−0.662827	+	0.662827i	−0.956045	−	0.293219i	$-0.905274\pi$
$421$	−13.6001	+	13.6001i	−0.662827	+	0.662827i	0.293219	+	0.956045i	$0.405274\pi$
$422$	−7.80977	−	15.8798i	−0.380174	−	0.773017i
$423$	−2.63009			−0.127879
$424$	−22.9385	−	4.63996i	−1.11399	−	0.225337i
$425$	−6.34117			−0.307592
$426$	11.3975	+	23.1749i	0.552213	+	1.12283i
$427$	24.4224	−	24.4224i	1.18188	−	1.18188i
$428$	2.55247	+	19.7166i	0.123378	+	0.953037i
$429$	7.36442	+	7.36442i	0.355557	+	0.355557i
$430$	−1.30396	−	0.444202i	−0.0628823	−	0.0214213i
$431$	−6.75253			−0.325258			−0.162629	−	0.986687i	$-0.551997\pi$
$431$	−6.75253			−0.325258			−0.162629	+	0.986687i	$0.551997\pi$
$432$	18.9998	+	11.0791i	0.914129	+	0.533045i
$433$		−	8.63103i		−	0.414781i	−0.978258	−	0.207390i	$-0.933503\pi$
$433$		−	8.63103i		−	0.414781i	0.978258	−	0.207390i	$-0.0664970\pi$
$434$	8.24283	+	2.80798i	0.395669	+	0.134788i
$435$	−0.124191	+	0.124191i	−0.00595448	+	0.00595448i
$436$	−1.13536	−	8.77010i	−0.0543739	−	0.420011i
$437$	7.46700	+	30.9666i	0.357195	+	1.48133i
$438$	−3.40634	+	1.67525i	−0.162761	+	0.0800467i
$439$	−23.6988			−1.13108			−0.565540	−	0.824721i	$-0.691332\pi$
$439$	−23.6988			−1.13108			−0.565540	+	0.824721i	$0.691332\pi$
$440$	−0.598888	−	0.902609i	−0.0285509	−	0.0430302i
$441$			0.108227i			0.00515369i
$442$	−1.48523	−	3.01996i	−0.0706452	−	0.143645i
$443$	−16.5520	+	16.5520i	−0.786407	+	0.786407i	−0.980903	−	0.194496i	$-0.937693\pi$
$443$	−16.5520	+	16.5520i	−0.786407	+	0.786407i	0.194496	+	0.980903i	$0.437693\pi$
$444$	−4.21760	−	3.25076i	−0.200158	−	0.154274i
$445$	−0.845142	+	0.845142i	−0.0400636	+	0.0400636i
$446$	3.80145	−	11.1592i	0.180004	−	0.528401i
$447$	11.3161			0.535232
$448$	−19.6009	−	8.26800i	−0.926056	−	0.390626i
$449$	−22.5417			−1.06381			−0.531904	−	0.846804i	$-0.678523\pi$
$449$	−22.5417			−1.06381			−0.531904	+	0.846804i	$0.678523\pi$
$450$	−10.1627	−	3.46199i	−0.479073	−	0.163200i
$451$	−7.94911	+	7.94911i	−0.374309	+	0.374309i
$452$	10.5850	−	13.7331i	0.497875	−	0.645953i
$453$	13.4224	+	13.4224i	0.630641	+	0.630641i
$454$	8.48073	−	4.17087i	0.398021	−	0.195749i
$455$	0.417597			0.0195772
$456$	12.6339	+	19.0411i	0.591639	+	0.891683i
$457$	19.8676			0.929365			0.464683	−	0.885477i	$-0.346168\pi$
$457$	19.8676			0.929365			0.464683	+	0.885477i	$0.346168\pi$
$458$	−28.2405	+	13.8888i	−1.31959	+	0.648981i
$459$	4.93789	+	4.93789i	0.230481	+	0.230481i
$460$	0.327821	−	0.733999i	0.0152847	−	0.0342229i
$461$	−28.8571	+	28.8571i	−1.34401	+	1.34401i	−0.451982	+	0.892027i	$0.649283\pi$
$461$	−28.8571	+	28.8571i	−1.34401	+	1.34401i	−0.892027	+	0.451982i	$0.850717\pi$
$462$	19.7860	+	6.74027i	0.920530	+	0.313586i
$463$		−	23.6252i		−	1.09796i	−0.835837	−	0.548978i	$-0.815017\pi$
$463$		−	23.6252i		−	1.09796i	0.835837	−	0.548978i	$-0.184983\pi$
$464$	−5.95314	−	3.47139i	−0.276368	−	0.161155i
$465$			0.236057i			0.0109469i
$466$	−2.30810	+	6.77544i	−0.106921	+	0.313866i
$467$	−2.66814	+	2.66814i	−0.123467	+	0.123467i	−0.766140	−	0.642674i	$-0.777825\pi$
$467$	−2.66814	+	2.66814i	−0.123467	+	0.123467i	0.642674	+	0.766140i	$0.277825\pi$
$468$	−0.731542	−	5.65080i	−0.0338155	−	0.261208i
$469$	0.640991	+	0.640991i	0.0295982	+	0.0295982i
$470$	0.0904821	+	0.183980i	0.00417363	+	0.00848634i
$471$			10.4170i			0.479988i
$472$	−40.0789	−	8.10711i	−1.84478	−	0.373160i
$473$			53.1089i			2.44195i
$474$	5.24169	+	10.6581i	0.240759	+	0.489541i
$475$	−23.4502	−	23.4502i	−1.07597	−	1.07597i
$476$	−5.34973	−	4.12336i	−0.245205	−	0.188994i
$477$	−8.89583	−	8.89583i	−0.407312	−	0.407312i
$478$	11.6037	−	34.0627i	0.530742	−	1.55799i
$479$	13.6769			0.624914			0.312457	−	0.949932i	$-0.398848\pi$
$479$	13.6769			0.624914			0.312457	+	0.949932i	$0.398848\pi$
$480$	0.0408200	−	0.575234i	0.00186317	−	0.0262557i
$481$			4.10147i			0.187011i
$482$	3.49903	−	10.2714i	0.159377	−	0.467850i
$483$	3.63625	+	15.0800i	0.165455	+	0.686163i
$484$	−12.0641	+	15.6522i	−0.548369	+	0.711465i
$485$	−0.473813	−	0.473813i	−0.0215147	−	0.0215147i
$486$	8.68064	+	17.6506i	0.393762	+	0.800646i
$487$	15.9805			0.724144			0.362072	−	0.932150i	$-0.382069\pi$
$487$	15.9805			0.724144			0.362072	+	0.932150i	$0.382069\pi$
$488$	−7.28359	+	36.0076i	−0.329712	+	1.62999i
$489$		−	18.5588i		−	0.839258i
$490$	0.00757071	−	0.00372331i	0.000342010	−	0.000168202i
$491$	23.4883	−	23.4883i	1.06001	−	1.06001i	0.0619296	−	0.998081i	$-0.480275\pi$
$491$	23.4883	−	23.4883i	1.06001	−	1.06001i	0.998081	−	0.0619296i	$-0.0197254\pi$
$492$	−5.93530	+	0.768373i	−0.267584	+	0.0346409i
$493$	−1.54717	−	1.54717i	−0.0696811	−	0.0696811i
$494$	5.67555	−	16.6606i	0.255355	−	0.749595i
$495$		−	0.582300i		−	0.0261724i
$496$	−8.95691	+	2.35862i	−0.402177	+	0.105905i
$497$		−	39.9231i		−	1.79079i
$498$	−16.0334	−	5.46189i	−0.718473	−	0.244753i
$499$	25.4995	+	25.4995i	1.14152	+	1.14152i	0.988173	+	0.153343i	$0.0490039\pi$
$499$	25.4995	+	25.4995i	1.14152	+	1.14152i	0.153343	+	0.988173i	$0.450996\pi$
$500$	0.215051	+	1.66116i	0.00961739	+	0.0742895i
$501$	−5.74511	−	5.74511i	−0.256673	−	0.256673i
$502$	15.8956	+	32.3210i	0.709457	+	1.44256i
$503$		−	19.6250i		−	0.875035i	−0.899210	−	0.437517i	$-0.855858\pi$
$503$		−	19.6250i		−	0.875035i	0.899210	−	0.437517i	$-0.144142\pi$
$504$	−6.32257	−	9.52901i	−0.281630	−	0.424456i
$505$	−0.432108			−0.0192286
$506$	−30.8621	−	2.83846i	−1.37199	−	0.126185i
$507$	−8.16150	+	8.16150i	−0.362465	+	0.362465i
$508$	6.37497	−	8.27102i	0.282844	−	0.366967i
$509$	12.6219	−	12.6219i	0.559456	−	0.559456i	−0.369697	−	0.929153i	$-0.620538\pi$
$509$	12.6219	−	12.6219i	0.559456	−	0.559456i	0.929153	+	0.369697i	$0.120538\pi$
$510$	0.0590422	−	0.173318i	0.00261443	−	0.00767466i
$511$	5.86805			0.259587
$512$	22.2344	−	4.19872i	0.982633	−	0.185559i
$513$			36.5215i			1.61246i
$514$	15.4376	+	5.25895i	0.680925	+	0.231962i
$515$	−0.789696	−	0.789696i	−0.0347982	−	0.0347982i
$516$	−17.2604	+	22.3940i	−0.759847	+	0.985841i
$517$	5.58929	−	5.58929i	0.245817	−	0.245817i
$518$	3.63279	+	7.38666i	0.159616	+	0.324551i
$519$	15.6695			0.687814
$520$	−0.370116	+	0.245575i	−0.0162307	+	0.0107692i
$521$	12.0617			0.528434			0.264217	−	0.964463i	$-0.414886\pi$
$521$	12.0617			0.528434			0.264217	+	0.964463i	$0.414886\pi$
$522$	−1.63488	−	3.32425i	−0.0715570	−	0.145499i
$523$	−1.82928	−	1.82928i	−0.0799888	−	0.0799888i	0.665980	−	0.745969i	$-0.268013\pi$
$523$	−1.82928	−	1.82928i	−0.0799888	−	0.0799888i	−0.745969	+	0.665980i	$0.768013\pi$
$524$	1.21088	+	9.35343i	0.0528974	+	0.408606i
$525$	−11.4197	−	11.4197i	−0.498396	−	0.498396i
$526$	−11.7838	+	34.5914i	−0.513799	+	1.50825i
$527$	−2.94081			−0.128104
$528$	−21.5001	+	5.66162i	−0.935672	+	0.246390i
$529$	−10.4825	−	20.4723i	−0.455761	−	0.890102i
$530$	−0.316239	+	0.928320i	−0.0137366	+	0.0403236i
$531$	−15.5431	−	15.5431i	−0.674513	−	0.674513i
$532$	−4.53522	−	35.0323i	−0.196627	−	1.51884i
$533$	3.25955	+	3.25955i	0.141187	+	0.141187i
$534$	10.8263	+	22.0134i	0.468501	+	0.952615i
$535$	0.833120			0.0360189
$536$	−0.945057	−	0.191165i	−0.0408202	−	0.00825707i
$537$			0.156488i			0.00675297i
$538$	−21.6915	+	10.6680i	−0.935186	+	0.459929i
$539$	−0.229998	−	0.229998i	−0.00990670	−	0.00990670i
$540$	0.562650	−	0.729994i	0.0242126	−	0.0314139i
$541$	−1.64738	+	1.64738i	−0.0708265	+	0.0708265i	−0.741633	−	0.670806i	$-0.765948\pi$
$541$	−1.64738	+	1.64738i	−0.0708265	+	0.0708265i	0.670806	+	0.741633i	$0.265948\pi$
$542$	8.97903	−	26.3579i	0.385682	−	1.13217i
$543$	19.4675			0.835431
$544$	7.16629	+	0.508537i	0.307252	+	0.0218034i
$545$	−0.370579			−0.0158738
$546$	2.76386	−	8.11330i	0.118282	−	0.347217i
$547$	−18.0346	−	18.0346i	−0.771105	−	0.771105i	0.207195	−	0.978300i	$-0.433567\pi$
$547$	−18.0346	−	18.0346i	−0.771105	−	0.771105i	−0.978300	+	0.207195i	$0.933567\pi$
$548$	−11.7618	−	9.06551i	−0.502438	−	0.387259i
$549$	−13.9642	+	13.9642i	−0.595979	+	0.595979i
$550$	28.9542	−	14.2398i	1.23461	−	0.607188i
$551$		−	11.4431i		−	0.487494i
$552$	−12.0909	−	11.2271i	−0.514621	−	0.477855i
$553$		−	18.3605i		−	0.780767i
$554$	7.59168	+	15.4364i	0.322540	+	0.655828i
$555$	−0.157787	+	0.157787i	−0.00669768	+	0.00669768i
$556$	18.6869	−	2.41918i	0.792503	−	0.102596i
$557$	−14.7445	−	14.7445i	−0.624743	−	0.624743i	0.321997	−	0.946741i	$-0.395646\pi$
$557$	−14.7445	−	14.7445i	−0.624743	−	0.624743i	−0.946741	+	0.321997i	$0.895646\pi$
$558$	−4.71308	−	1.60555i	−0.199521	−	0.0679683i
$559$	21.7774			0.921086
$560$	−0.449058	+	0.770098i	−0.0189762	+	0.0325426i
$561$	−7.05910			−0.298035
$562$	38.3577	+	13.0668i	1.61802	+	0.551192i
$563$	−7.74891	+	7.74891i	−0.326578	+	0.326578i	−0.851284	−	0.524706i	$-0.824175\pi$
$563$	−7.74891	+	7.74891i	−0.326578	+	0.326578i	0.524706	+	0.851284i	$0.324175\pi$
$564$	4.17331	−	0.540269i	0.175728	−	0.0227494i
$565$	−0.513779	−	0.513779i	−0.0216148	−	0.0216148i
$566$	−3.53226	−	7.18223i	−0.148472	−	0.301892i
$567$			5.65561i			0.237513i
$568$	23.4775	+	35.3839i	0.985092	+	1.48467i
$569$	3.63750			0.152492			0.0762460	−	0.997089i	$-0.475707\pi$
$569$	3.63750			0.152492			0.0762460	+	0.997089i	$0.475707\pi$
$570$	0.859289	−	0.422603i	0.0359917	−	0.0177009i
$571$	−12.0122	−	12.0122i	−0.502695	−	0.502695i	0.409579	−	0.912275i	$-0.365676\pi$
$571$	−12.0122	−	12.0122i	−0.502695	−	0.502695i	−0.912275	+	0.409579i	$0.865676\pi$
$572$	13.5633	+	10.4541i	0.567111	+	0.437106i
$573$	−13.5503	−	13.5503i	−0.566072	−	0.566072i
$574$	8.75745	+	2.98329i	0.365529	+	0.124520i
$575$	20.4293	+	12.4912i	0.851961	+	0.520918i
$576$	11.2074	+	4.72747i	0.466975	+	0.196978i
$577$	−20.4216			−0.850164			−0.425082	−	0.905155i	$-0.639755\pi$
$577$	−20.4216			−0.850164			−0.425082	+	0.905155i	$0.639755\pi$
$578$	−20.5982	−	7.01693i	−0.856772	−	0.291866i
$579$	−8.55781	−	8.55781i	−0.355650	−	0.355650i
$580$	−0.176293	+	0.228726i	−0.00732018	+	0.00949734i
$581$	18.5148	+	18.5148i	0.768123	+	0.768123i
$582$	−12.3414	+	6.06957i	−0.511568	+	0.251592i
$583$	37.8097			1.56592
$584$	−5.20086	+	3.45081i	−0.215213	+	0.142795i
$585$	−0.238773			−0.00987206
$586$	17.8518	−	8.77960i	0.737451	−	0.362682i
$587$	−17.0110	+	17.0110i	−0.702118	+	0.702118i	−0.964865	−	0.262747i	$-0.915372\pi$
$587$	−17.0110	+	17.0110i	−0.702118	+	0.702118i	0.262747	+	0.964865i	$0.415372\pi$
$588$	−0.0222319	−	0.171731i	−0.000916829	−	0.00708205i
$589$	−10.8754	−	10.8754i	−0.448112	−	0.448112i
$590$	−0.552544	+	1.62199i	−0.0227479	+	0.0667764i
$591$			20.6833i			0.850799i
$592$	−7.56360	−	4.41047i	−0.310862	−	0.181269i
$593$	−3.97528			−0.163245			−0.0816226	−	0.996663i	$-0.526010\pi$
$593$	−3.97528			−0.163245			−0.0816226	+	0.996663i	$0.526010\pi$
$594$	−33.6353	−	11.4581i	−1.38007	−	0.470133i
$595$	−0.200142	+	0.200142i	−0.00820502	+	0.00820502i
$596$	18.4524	−	2.38881i	0.755840	−	0.0978497i
$597$	−10.4290	+	10.4290i	−0.426831	+	0.426831i
$598$	−1.16391	+	12.6551i	−0.0475960	+	0.517504i
$599$	−22.1613			−0.905487			−0.452744	−	0.891641i	$-0.649555\pi$
$599$	−22.1613			−0.905487			−0.452744	+	0.891641i	$0.649555\pi$
$600$	16.8368	+	3.40573i	0.687360	+	0.139038i
$601$		−	16.7533i		−	0.683381i	−0.939813	−	0.341690i	$-0.889001\pi$
$601$		−	16.7533i		−	0.683381i	0.939813	−	0.341690i	$-0.110999\pi$
$602$	39.2206	−	19.2889i	1.59851	−	0.786157i
$603$	−0.366505	−	0.366505i	−0.0149253	−	0.0149253i
$604$	24.7206	+	19.0537i	1.00587	+	0.775282i
$605$	0.585575	+	0.585575i	0.0238070	+	0.0238070i
$606$	−2.85990	+	8.39524i	−0.116176	+	0.341033i
$607$			36.1916i			1.46897i	0.678624	+	0.734486i	$0.262577\pi$
$607$			36.1916i			1.46897i	−0.678624	+	0.734486i	$0.737423\pi$
$608$	24.6209	+	28.3822i	0.998511	+	1.15105i
$609$		−	5.57253i		−	0.225810i
$610$	1.45723	+	0.496417i	0.0590015	+	0.0200993i
$611$	−2.29190	−	2.29190i	−0.0927203	−	0.0927203i
$612$	3.05887	+	2.35765i	0.123647	+	0.0953025i
$613$	−30.4776	+	30.4776i	−1.23098	+	1.23098i	−0.267392	+	0.963588i	$0.586162\pi$
$613$	−30.4776	+	30.4776i	−1.23098	+	1.23098i	−0.963588	+	0.267392i	$0.913838\pi$
$614$	−9.48446	−	19.2850i	−0.382762	−	0.778279i
$615$			0.250795i			0.0101130i
$616$	33.6867	+	6.81411i	1.35728	+	0.274548i
$617$	−16.7959			−0.676176			−0.338088	−	0.941114i	$-0.609780\pi$
$617$	−16.7959			−0.676176			−0.338088	+	0.941114i	$0.609780\pi$
$618$	−20.5692	+	10.1161i	−0.827416	+	0.406928i
$619$	10.5813	+	10.5813i	0.425300	+	0.425300i	0.887024	−	0.461724i	$-0.152769\pi$
$619$	10.5813	+	10.5813i	0.425300	+	0.425300i	−0.461724	+	0.887024i	$0.652769\pi$
$620$	0.0498315	+	0.384924i	0.00200128	+	0.0154589i
$621$	−6.18144	−	25.6353i	−0.248053	−	1.02871i
$622$	−18.9076	−	6.44102i	−0.758126	−	0.258261i
$623$		−	37.9222i		−	1.51932i
$624$	2.32156	+	8.81616i	0.0929366	+	0.352929i
$625$	−24.8947			−0.995787
$626$	−32.6244	−	11.1137i	−1.30393	−	0.444194i
$627$	−26.1052	−	26.1052i	−1.04254	−	1.04254i
$628$	2.19901	+	16.9863i	0.0877502	+	0.677826i
$629$	−1.96571	−	1.96571i	−0.0783782	−	0.0783782i
$630$	−0.430025	+	0.211489i	−0.0171326	+	0.00842591i
$631$			44.3752i			1.76655i	0.468857	+	0.883274i	$0.344666\pi$
$631$			44.3752i			1.76655i	−0.468857	+	0.883274i	$0.655334\pi$
$632$	10.7972	+	16.2729i	0.429489	+	0.647301i
$633$			15.2206i			0.604965i
$634$	−18.8527	+	9.27187i	−0.748737	+	0.368233i
$635$	−0.309432	−	0.309432i	−0.0122794	−	0.0122794i
$636$	15.9429	+	12.2881i	0.632176	+	0.487257i
$637$	−0.0943110	+	0.0943110i	−0.00373674	+	0.00373674i
$638$	10.5388	+	3.59013i	0.417236	+	0.142135i
$639$			22.8272i			0.903029i
$640$	−0.0548690	−	0.946615i	−0.00216889	−	0.0374183i
$641$		−	22.6166i		−	0.893303i	−0.894708	−	0.446652i	$-0.852616\pi$
$641$		−	22.6166i		−	0.893303i	0.894708	−	0.446652i	$-0.147384\pi$
$642$	5.51399	−	16.1863i	0.217620	−	0.638823i
$643$	25.9171	−	25.9171i	1.02207	−	1.02207i	0.0223210	−	0.999751i	$-0.492894\pi$
$643$	25.9171	−	25.9171i	1.02207	−	1.02207i	0.999751	−	0.0223210i	$-0.00710559\pi$
$644$	9.11278	+	23.8224i	0.359094	+	0.938733i
$645$	0.837795	+	0.837795i	0.0329881	+	0.0329881i
$646$	5.26480	+	10.7051i	0.207141	+	0.421185i
$647$	−16.0802			−0.632179			−0.316090	−	0.948729i	$-0.602370\pi$
$647$	−16.0802			−0.632179			−0.316090	+	0.948729i	$0.602370\pi$
$648$	−3.32588	−	5.01257i	−0.130653	−	0.196912i
$649$	66.0623			2.59317
$650$	−5.83906	−	11.8727i	−0.229027	−	0.465686i
$651$	−5.29604	−	5.29604i	−0.207568	−	0.207568i
$652$	−3.91775	−	30.2627i	−0.153431	−	1.18518i
$653$	25.6456	−	25.6456i	1.00359	−	1.00359i	0.00359817	−	0.999994i	$-0.498855\pi$
$653$	25.6456	−	25.6456i	1.00359	−	1.00359i	0.999994	−	0.00359817i	$-0.00114534\pi$
$654$	−2.45267	+	7.19980i	−0.0959070	+	0.281535i
$655$	0.395227			0.0154428
$656$	−9.51611	+	2.50587i	−0.371542	+	0.0978380i
$657$	−3.35523			−0.130900
$658$	−6.15766	−	2.09765i	−0.240051	−	0.0817751i
$659$	−5.67720	+	5.67720i	−0.221152	+	0.221152i	−0.808984	−	0.587831i	$-0.799982\pi$
$659$	−5.67720	+	5.67720i	−0.221152	+	0.221152i	0.587831	+	0.808984i	$0.299982\pi$
$660$	0.119615	+	0.923968i	0.00465602	+	0.0359654i
$661$	25.6539	−	25.6539i	0.997820	−	0.997820i	−0.00217783	−	0.999998i	$-0.500693\pi$
$661$	25.6539	−	25.6539i	0.997820	−	0.997820i	0.999998	+	0.00217783i	$0.000693226\pi$
$662$	15.8574	−	7.79873i	0.616314	−	0.303106i
$663$			2.89460i			0.112417i
$664$	−27.2976	−	5.52173i	−1.05935	−	0.214285i
$665$	−1.48028			−0.0574030
$666$	−2.07716	−	4.22354i	−0.0804882	−	0.163659i
$667$	1.93681	+	8.03220i	0.0749936	+	0.311008i
$668$	−10.5810	−	8.15540i	−0.409390	−	0.315542i
$669$	−7.16979	+	7.16979i	−0.277200	+	0.277200i
$670$	−0.0130290	+	0.0382465i	−0.000503353	+	0.00147759i
$671$		−	59.3517i		−	2.29125i
$672$	11.9898	+	13.8214i	0.462517	+	0.533173i
$673$	−14.3871			−0.554583			−0.277291	−	0.960786i	$-0.589437\pi$
$673$	−14.3871			−0.554583			−0.277291	+	0.960786i	$0.589437\pi$
$674$	−4.85643	+	14.2560i	−0.187063	+	0.549122i
$675$	19.4129	+	19.4129i	0.747203	+	0.747203i
$676$	−11.5856	+	15.0313i	−0.445598	+	0.578128i
$677$	−9.48874	+	9.48874i	−0.364682	+	0.364682i	−0.865533	−	0.500851i	$-0.833020\pi$
$677$	−9.48874	+	9.48874i	−0.364682	+	0.364682i	0.500851	+	0.865533i	$0.333020\pi$
$678$	−13.3824	+	6.58154i	−0.513948	+	0.252762i
$679$	21.2604			0.815898
$680$	0.0596890	−	0.295083i	0.00228897	−	0.0113159i
$681$	−8.12869			−0.311492
$682$	13.4279	−	6.60392i	0.514182	−	0.252877i
$683$	−10.0685	+	10.0685i	−0.385260	+	0.385260i	−0.872993	−	0.487733i	$-0.837824\pi$
$683$	−10.0685	+	10.0685i	−0.385260	+	0.385260i	0.487733	+	0.872993i	$0.337824\pi$
$684$	2.59315	+	20.0308i	0.0991514	+	0.765895i
$685$	−0.440026	+	0.440026i	−0.0168125	+	0.0168125i
$686$	8.40228	−	24.6649i	0.320801	−	0.941709i
$687$	27.0682			1.03272
$688$	−23.4181	+	40.1602i	−0.892807	+	1.53109i
$689$		−	15.5039i		−	0.590652i
$690$	−0.531627	+	0.442074i	−0.0202387	+	0.0168295i
$691$	−25.0974	−	25.0974i	−0.954750	−	0.954750i	0.0442700	−	0.999020i	$-0.485904\pi$
$691$	−25.0974	−	25.0974i	−0.954750	−	0.954750i	−0.999020	+	0.0442700i	$0.985904\pi$
$692$	25.5512	−	3.30782i	0.971312	−	0.125744i
$693$	13.0641	+	13.0641i	0.496266	+	0.496266i
$694$	29.4826	−	14.4997i	1.11914	−	0.550400i
$695$		−	0.789613i		−	0.0299517i
$696$	3.27703	+	4.93894i	0.124215	+	0.187210i
$697$	−3.12441			−0.118346
$698$	9.92540	−	4.88136i	0.375682	−	0.184762i
$699$	4.35324	−	4.35324i	0.164655	−	0.164655i
$700$	−21.0320	−	16.2107i	−0.794937	−	0.612706i
$701$	1.25488	+	1.25488i	0.0473963	+	0.0473963i	0.730408	−	0.683011i	$-0.239330\pi$
$701$	1.25488	+	1.25488i	0.0473963	+	0.0473963i	−0.683011	+	0.730408i	$0.739330\pi$
$702$	−4.69842	+	13.7922i	−0.177331	+	0.520553i
$703$		−	14.5388i		−	0.548340i
$704$	−33.8637	+	13.7707i	−1.27629	+	0.519003i
$705$		−	0.176342i		−	0.00664144i
$706$	−43.1119	−	14.6864i	−1.62254	−	0.552730i
$707$	9.69453	−	9.69453i	0.364600	−	0.364600i
$708$	27.8559	+	21.4703i	1.04689	+	0.806902i
$709$	17.0708	−	17.0708i	0.641106	−	0.641106i	−0.309721	−	0.950827i	$-0.600236\pi$
$709$	17.0708	−	17.0708i	0.641106	−	0.641106i	0.950827	+	0.309721i	$0.100236\pi$
$710$	1.59680	−	0.785316i	0.0599270	−	0.0294724i
$711$			10.4981i			0.393711i
$712$	22.3008	+	33.6105i	0.835758	+	1.25961i
$713$	9.47438	+	5.79296i	0.354818	+	0.216948i
$714$	2.56383	+	5.21310i	0.0959489	+	0.195095i
$715$	0.507425	−	0.507425i	0.0189766	−	0.0189766i
$716$	0.0330346	+	0.255176i	0.00123456	+	0.00953636i
$717$	−21.8854	+	21.8854i	−0.817325	+	0.817325i
$718$	6.23705	−	18.3088i	0.232765	−	0.683280i
$719$			10.8401i			0.404268i	0.979358	+	0.202134i	$0.0647876\pi$
$719$			10.8401i			0.404268i	−0.979358	+	0.202134i	$0.935212\pi$
$720$	0.256762	−	0.440326i	0.00956896	−	0.0164100i
$721$	35.4343			1.31964
$722$	−11.4540	+	33.6232i	−0.426273	+	1.25132i
$723$	−6.59940	+	6.59940i	−0.245434	+	0.245434i
$724$	31.7445	−	4.10958i	1.17977	−	0.152731i
$725$	−6.08258	−	6.08258i	−0.225901	−	0.225901i
$726$	15.2525	−	7.50125i	0.566073	−	0.278397i
$727$			10.3403i			0.383501i	0.981444	+	0.191751i	$0.0614165\pi$
$727$			10.3403i			0.383501i	−0.981444	+	0.191751i	$0.938583\pi$
$728$	2.79414	−	13.8133i	0.103558	−	0.511955i
$729$		−	23.2984i		−	0.862903i
$730$	0.115429	+	0.234704i	0.00427221	+	0.00868680i
$731$	−10.4373	+	10.4373i	−0.386037	+	0.386037i
$732$	19.2893	−	25.0263i	0.712954	−	0.925000i
$733$	18.2971	+	18.2971i	0.675819	+	0.675819i	0.959051	−	0.283232i	$-0.0914068\pi$
$733$	18.2971	+	18.2971i	0.675819	+	0.675819i	−0.283232	+	0.959051i	$0.591407\pi$
$734$	24.7404	+	8.42800i	0.913184	+	0.311083i
$735$	−0.00725644			−0.000267658
$736$	−22.0858	−	15.7549i	−0.814094	−	0.580732i
$737$	1.55775			0.0573803
$738$	−5.00733	−	1.70579i	−0.184322	−	0.0627908i
$739$	29.3914	+	29.3914i	1.08118	+	1.08118i	0.996400	+	0.0847802i	$0.0270188\pi$
$739$	29.3914	+	29.3914i	1.08118	+	1.08118i	0.0847802	+	0.996400i	$0.472981\pi$
$740$	−0.223984	+	0.290602i	−0.00823383	+	0.0106827i
$741$	−10.7045	+	10.7045i	−0.393238	+	0.393238i
$742$	−13.7323	−	27.9222i	−0.504128	−	1.02506i
$743$		−	15.4325i		−	0.566163i	−0.959096	−	0.283081i	$-0.908643\pi$
$743$		−	15.4325i		−	0.566163i	0.959096	−	0.283081i	$-0.0913566\pi$
$744$	7.80832	+	1.57946i	0.286267	+	0.0579057i
$745$		−	0.779703i		−	0.0285661i
$746$	4.82445	−	2.37269i	0.176636	−	0.0868704i
$747$	−10.5864	−	10.5864i	−0.387335	−	0.387335i
$748$	−11.5108	+	1.49017i	−0.420878	+	0.0544861i
$749$	−18.6914	+	18.6914i	−0.682969	+	0.682969i
$750$	0.464566	−	1.36373i	0.0169635	−	0.0497965i
$751$	14.9635			0.546026			0.273013	−	0.962010i	$-0.411980\pi$
$751$	14.9635			0.546026			0.273013	+	0.962010i	$0.411980\pi$
$752$	6.69110	−	1.76197i	0.243999	−	0.0642523i
$753$		−	30.9793i		−	1.12895i
$754$	1.47214	−	4.32146i	0.0536122	−	0.157378i
$755$	0.924836	−	0.924836i	0.0336582	−	0.0336582i
$756$	3.75442	+	29.0010i	0.136547	+	1.05476i
$757$	11.8442	−	11.8442i	0.430485	−	0.430485i	−0.458308	−	0.888793i	$-0.651544\pi$
$757$	11.8442	−	11.8442i	0.430485	−	0.430485i	0.888793	+	0.458308i	$0.151544\pi$
$758$	−15.1445	−	30.7936i	−0.550072	−	1.11848i
$759$	22.7422	+	13.9054i	0.825491	+	0.504733i
$760$	1.31198	−	0.870507i	0.0475904	−	0.0315766i
$761$		−	0.408106i		−	0.0147938i	−0.999973	−	0.00739692i	$-0.997645\pi$
$761$		−	0.408106i		−	0.0147938i	0.999973	−	0.00739692i	$-0.00235453\pi$
$762$	−8.05978	+	3.96384i	−0.291975	+	0.143595i
$763$	8.31408	−	8.31408i	0.300990	−	0.300990i
$764$	−24.9561	−	19.2351i	−0.902879	−	0.695903i
$765$	0.114437	−	0.114437i	0.00413748	−	0.00413748i
$766$	−12.3175	−	4.19605i	−0.445049	−	0.151610i
$767$		−	27.0890i		−	0.978126i
$768$	−18.7545	−	5.19914i	−0.676745	−	0.187608i
$769$		−	44.9499i		−	1.62093i	−0.585784	−	0.810467i	$-0.699213\pi$
$769$		−	44.9499i		−	1.62093i	0.585784	−	0.810467i	$-0.300787\pi$
$770$	0.464419	−	1.36330i	0.0167365	−	0.0491300i
$771$	−9.91873	−	9.91873i	−0.357214	−	0.357214i
$772$	−15.7612	−	12.1481i	−0.567259	−	0.437221i
$773$	−28.2917	+	28.2917i	−1.01758	+	1.01758i	−0.0177385	+	0.999843i	$0.505647\pi$
$773$	−28.2917	+	28.2917i	−1.01758	+	1.01758i	−0.999843	+	0.0177385i	$0.994353\pi$
$774$	−22.4255	+	11.0290i	−0.806070	+	0.396429i
$775$	−11.5616			−0.415303
$776$	−18.8431	+	12.5025i	−0.676427	+	0.448815i
$777$		−	7.08003i		−	0.253995i
$778$	34.3565	−	16.8967i	1.23174	−	0.605777i
$779$	−11.5543	−	11.5543i	−0.413977	−	0.413977i
$780$	0.378875	−	0.0490484i	0.0135659	−	0.00175622i
$781$	−48.5108	−	48.5108i	−1.73585	−	1.73585i
$782$	−5.50737	−	6.62303i	−0.196943	−	0.236839i
$783$			9.47304i			0.338539i
$784$	−0.0725044	−	0.275337i	−0.00258944	−	0.00983346i
$785$	0.717752			0.0256177
$786$	2.61581	−	7.67869i	0.0933027	−	0.273890i
$787$	23.2407	−	23.2407i	0.828442	−	0.828442i	−0.158859	−	0.987301i	$-0.550782\pi$
$787$	23.2407	−	23.2407i	0.828442	−	0.828442i	0.987301	+	0.158859i	$0.0507815\pi$
$788$	4.36624	+	33.7270i	0.155541	+	1.20148i
$789$	22.2250	−	22.2250i	0.791232	−	0.791232i
$790$	0.734364	−	0.361164i	0.0261275	−	0.0128496i
$791$	23.0537			0.819694
$792$	−19.2614	−	3.89617i	−0.684423	−	0.138444i
$793$	−24.3373			−0.864242
$794$	−7.95377	+	3.91171i	−0.282269	+	0.138821i
$795$	0.596448	−	0.596448i	0.0211538	−	0.0211538i
$796$	−14.8044	+	19.2075i	−0.524728	+	0.680792i
$797$	16.5321	+	16.5321i	0.585598	+	0.585598i	0.936436	−	0.350838i	$-0.114103\pi$
$797$	16.5321	+	16.5321i	0.585598	+	0.585598i	−0.350838	+	0.936436i	$0.614103\pi$
$798$	−9.79724	+	28.7598i	−0.346819	+	1.01808i
$799$	2.19688			0.0777200
$800$	28.1737	+	1.99927i	0.996090	+	0.0706850i
$801$			21.6831i			0.766136i
$802$	4.17089	−	12.2436i	0.147279	−	0.432337i
$803$	7.13030	−	7.13030i	0.251623	−	0.251623i
$804$	0.656841	+	0.506267i	0.0231650	+	0.0178547i
$805$	1.03905	−	0.250546i	0.0366215	−	0.00883057i
$806$	−2.70795	−	5.50614i	−0.0953835	−	0.193946i
$807$	20.7910			0.731879
$808$	−2.89123	+	14.2933i	−0.101713	+	0.502837i
$809$		−	3.22326i		−	0.113324i	−0.998393	−	0.0566618i	$-0.981954\pi$
$809$		−	3.22326i		−	0.113324i	0.998393	−	0.0566618i	$-0.0180457\pi$
$810$	−0.226207	+	0.111250i	−0.00794812	+	0.00390892i
$811$	−12.6982	+	12.6982i	−0.445893	+	0.445893i	−0.893987	−	0.448093i	$-0.852103\pi$
$811$	−12.6982	+	12.6982i	−0.445893	+	0.445893i	0.448093	+	0.893987i	$0.352103\pi$
$812$	−1.17636	−	9.08678i	−0.0412821	−	0.318883i
$813$	−16.9350	+	16.9350i	−0.593937	+	0.593937i
$814$	13.3898	+	4.56134i	0.469313	+	0.159875i
$815$	−1.27874			−0.0447924
$816$	−5.33798	−	3.11267i	−0.186867	−	0.108965i
$817$	−77.1959			−2.70074
$818$	−17.6165	+	51.7133i	−0.615948	+	1.80811i
$819$	5.35698	−	5.35698i	0.187188	−	0.187188i
$820$	0.0529426	+	0.408955i	0.00184884	+	0.0142813i
$821$	−24.5612	−	24.5612i	−0.857192	−	0.857192i	0.133814	−	0.991006i	$-0.457277\pi$
$821$	−24.5612	−	24.5612i	−0.857192	−	0.857192i	−0.991006	+	0.133814i	$0.957277\pi$
$822$	5.63676	+	11.4614i	0.196605	+	0.399761i
$823$	−45.6245			−1.59037			−0.795185	−	0.606367i	$-0.792626\pi$
$823$	−45.6245			−1.59037			−0.795185	+	0.606367i	$0.792626\pi$
$824$	−31.4055	+	20.8378i	−1.09406	+	0.725918i
$825$	−27.7523			−0.966210
$826$	−23.9935	−	48.7866i	−0.834841	−	1.69750i
$827$	0.390922	+	0.390922i	0.0135937	+	0.0135937i	0.713871	−	0.700277i	$-0.246940\pi$
$827$	0.390922	+	0.390922i	0.0135937	+	0.0135937i	−0.700277	+	0.713871i	$0.746940\pi$
$828$	−5.21050	−	13.6211i	−0.181077	−	0.473368i
$829$	−12.4079	+	12.4079i	−0.430943	+	0.430943i	−0.888949	−	0.458006i	$-0.848564\pi$
$829$	−12.4079	+	12.4079i	−0.430943	+	0.430943i	0.458006	+	0.888949i	$0.348564\pi$
$830$	−0.376337	+	1.10474i	−0.0130628	+	0.0383459i
$831$		−	14.7956i		−	0.513253i
$832$	5.64670	+	13.8859i	0.195764	+	0.481406i
$833$		−	0.0904010i		−	0.00313221i
$834$	−15.3410	−	5.22604i	−0.531217	−	0.180963i
$835$	−0.395851	+	0.395851i	−0.0136990	+	0.0136990i
$836$	−48.0788	−	37.0573i	−1.66284	−	1.28165i
$837$	9.00301	+	9.00301i	0.311190	+	0.311190i
$838$	21.7271	−	10.6855i	0.750549	−	0.369124i
$839$		−	2.88285i		−	0.0995269i	−0.998761	−	0.0497635i	$-0.984153\pi$
$839$		−	2.88285i		−	0.0995269i	0.998761	−	0.0497635i	$-0.0158467\pi$
$840$	0.638901	−	0.423916i	0.0220442	−	0.0146265i
$841$			26.0318i			0.897650i
$842$	24.4080	−	12.0040i	0.841156	−	0.413685i
$843$	−24.6449	−	24.6449i	−0.848816	−	0.848816i
$844$	3.21306	+	24.8193i	0.110598	+	0.854315i
$845$	0.562346	+	0.562346i	0.0193453	+	0.0193453i
$846$	3.52082	+	1.19940i	0.121048	+	0.0412361i
$847$	−26.2752			−0.902827
$848$	28.5911	+	16.6720i	0.981821	+	0.572518i
$849$			6.88409i			0.236261i
$850$	8.48874	+	2.89176i	0.291161	+	0.0991864i
$851$	2.46076	+	10.2051i	0.0843538	+	0.349826i
$852$	−4.68913	−	36.2212i	−0.160647	−	1.24092i
$853$	−4.58595	−	4.58595i	−0.157020	−	0.157020i	0.624225	−	0.781245i	$-0.285415\pi$
$853$	−4.58595	−	4.58595i	−0.157020	−	0.157020i	−0.781245	+	0.624225i	$0.785415\pi$
$854$	−43.8309	+	21.5562i	−1.49986	+	0.737640i
$855$	0.846396			0.0289461
$856$	5.57440	−	27.5580i	0.190529	−	0.941913i
$857$			18.1650i			0.620506i	0.950654	+	0.310253i	$0.100414\pi$
$857$			18.1650i			0.620506i	−0.950654	+	0.310253i	$0.899586\pi$
$858$	−6.50014	−	13.2169i	−0.221911	−	0.451218i
$859$	24.8997	−	24.8997i	0.849566	−	0.849566i	−0.140513	−	0.990079i	$-0.544875\pi$
$859$	24.8997	−	24.8997i	0.849566	−	0.849566i	0.990079	+	0.140513i	$0.0448750\pi$
$860$	1.54300	+	1.18928i	0.0526158	+	0.0405542i
$861$	−5.62669	−	5.62669i	−0.191757	−	0.191757i
$862$	9.03941	+	3.07934i	0.307883	+	0.104883i
$863$		−	17.1216i		−	0.582825i	−0.956598	−	0.291412i	$-0.905875\pi$
$863$		−	17.1216i		−	0.582825i	0.956598	−	0.291412i	$-0.0941252\pi$
$864$	−20.3821	−	23.4958i	−0.693413	−	0.799342i
$865$		−	1.07966i		−	0.0367096i
$866$	−3.93599	+	11.5541i	−0.133751	+	0.392624i
$867$	13.2344	+	13.2344i	0.449464	+	0.449464i
$868$	−9.75391	−	7.51793i	−0.331069	−	0.255175i
$869$	−22.3099	−	22.3099i	−0.756813	−	0.756813i
$870$	0.222885	−	0.109616i	0.00755650	−	0.00371632i
$871$		−	0.638756i		−	0.0216434i
$872$	−2.47954	+	12.2580i	−0.0839678	+	0.415109i
$873$	−12.1562			−0.411426
$874$	4.12581	−	44.8593i	0.139558	−	1.51739i
$875$	−1.57479	+	1.57479i	−0.0532376	+	0.0532376i
$876$	5.32393	−	0.689226i	0.179879	−	0.0232868i
$877$	−15.2309	+	15.2309i	−0.514312	+	0.514312i	−0.915845	−	0.401532i	$-0.868478\pi$
$877$	−15.2309	+	15.2309i	−0.514312	+	0.514312i	0.401532	+	0.915845i	$0.368478\pi$
$878$	31.7248	+	10.8073i	1.07066	+	0.364729i
$879$	−17.1107			−0.577131
$880$	0.390098	+	1.48141i	0.0131502	+	0.0499382i
$881$		−	51.1387i		−	1.72291i	−0.507837	−	0.861453i	$-0.669555\pi$
$881$		−	51.1387i		−	1.72291i	0.507837	−	0.861453i	$-0.330445\pi$
$882$	0.0493548	−	0.144881i	0.00166186	−	0.00487839i
$883$	−2.24931	−	2.24931i	−0.0756953	−	0.0756953i	0.668245	−	0.743941i	$-0.267046\pi$
$883$	−2.24931	−	2.24931i	−0.0756953	−	0.0756953i	−0.743941	+	0.668245i	$0.767046\pi$
$884$	0.611047	+	4.72004i	0.0205517	+	0.158752i
$885$	1.04213	−	1.04213i	0.0350310	−	0.0350310i
$886$	29.7058	−	14.6095i	0.997985	−	0.490814i
$887$	41.9597			1.40887			0.704435	−	0.709769i	$-0.251201\pi$
$887$	41.9597			1.40887			0.704435	+	0.709769i	$0.251201\pi$
$888$	4.16353	+	6.27504i	0.139719	+	0.210576i
$889$	13.8845			0.465670
$890$	1.51678	−	0.745958i	0.0508424	−	0.0250046i
$891$	6.87217	+	6.87217i	0.230226	+	0.230226i
$892$	−10.1778	+	13.2049i	−0.340777	+	0.442131i
$893$	8.12425	+	8.12425i	0.271868	+	0.271868i
$894$	−15.1485	−	5.16045i	−0.506641	−	0.172591i
$895$	0.0107824			0.000360416
$896$	22.4687	+	20.0067i	0.750627	+	0.668377i
$897$	5.70192	−	9.32549i	0.190382	−	0.311369i
$898$	30.1759	+	10.2797i	1.00698	+	0.343037i
$899$	−2.82088	−	2.82088i	−0.0940817	−	0.0940817i
$900$	12.0257	+	9.26893i	0.400856	+	0.308964i
$901$	7.43057	+	7.43057i	0.247548	+	0.247548i
$902$	14.2663	−	7.01622i	0.475014	−	0.233614i
$903$	−37.5925			−1.25100
$904$	−20.4325	+	13.5571i	−0.679574	+	0.450903i
$905$		−	1.34136i		−	0.0445882i
$906$	−11.8472	−	24.0892i	−0.393597	−	0.800311i
$907$	−6.73858	−	6.73858i	−0.223751	−	0.223751i	0.586325	−	0.810076i	$-0.300574\pi$
$907$	−6.73858	−	6.73858i	−0.223751	−	0.223751i	−0.810076	+	0.586325i	$0.800574\pi$
$908$	−13.2549	+	1.71596i	−0.439881	+	0.0569462i
$909$	−5.54313	+	5.54313i	−0.183854	+	0.183854i
$910$	−0.559024	−	0.190436i	−0.0185315	−	0.00631289i
$911$	58.1801			1.92759			0.963796	−	0.266642i	$-0.0859142\pi$
$911$	58.1801			1.92759			0.963796	+	0.266642i	$0.0859142\pi$
$912$	−8.22938	−	31.2513i	−0.272502	−	1.03483i
$913$	44.9949			1.48911
$914$	−26.5961	−	9.06017i	−0.879721	−	0.299684i
$915$	−0.936275	−	0.936275i	−0.0309523	−	0.0309523i
$916$	44.1384	−	5.71407i	1.45837	−	0.188798i
$917$	−8.86708	+	8.86708i	−0.292817	+	0.292817i
$918$	−4.35839	−	8.86202i	−0.143848	−	0.292490i
$919$			45.9219i			1.51482i	0.652938	+	0.757411i	$0.273536\pi$
$919$			45.9219i			1.51482i	−0.652938	+	0.757411i	$0.726464\pi$
$920$	−0.773569	+	0.833087i	−0.0255038	+	0.0274661i
$921$			18.4845i			0.609083i
$922$	51.7898	−	25.4705i	1.70561	−	0.838826i
$923$	−19.8919	+	19.8919i	−0.654751	+	0.654751i
$924$	−23.4132	−	18.0460i	−0.770238	−	0.593669i
$925$	−7.72805	−	7.72805i	−0.254097	−	0.254097i
$926$	−10.7738	+	31.6263i	−0.354048	+	1.03931i
$927$	−20.2606			−0.665446
$928$	6.38625	+	7.36184i	0.209639	+	0.241664i
$929$	18.0479			0.592132			0.296066	−	0.955167i	$-0.404325\pi$
$929$	18.0479			0.592132			0.296066	+	0.955167i	$0.404325\pi$
$930$	0.107649	−	0.316003i	0.00352994	−	0.0103621i
$931$	0.334311	−	0.334311i	0.0109566	−	0.0109566i
$932$	6.17958	−	8.01751i	0.202419	−	0.262622i
$933$	12.1482	+	12.1482i	0.397714	+	0.397714i
$934$	4.78850	−	2.35501i	0.156685	−	0.0770583i
$935$			0.486388i			0.0159066i
$936$	−1.59763	+	7.89816i	−0.0522202	+	0.258159i
$937$	3.77047			0.123176			0.0615879	−	0.998102i	$-0.480384\pi$
$937$	3.77047			0.123176			0.0615879	+	0.998102i	$0.480384\pi$
$938$	−0.565765	−	1.15039i	−0.0184729	−	0.0375614i
$939$	20.9612	+	20.9612i	0.684044	+	0.684044i
$940$	−0.0372257	−	0.287550i	−0.00121417	−	0.00937886i
$941$	19.3322	+	19.3322i	0.630212	+	0.630212i	0.948121	−	0.317909i	$-0.102981\pi$
$941$	19.3322	+	19.3322i	0.630212	+	0.630212i	−0.317909	+	0.948121i	$0.602981\pi$
$942$	4.75043	−	13.9449i	0.154777	−	0.454348i
$943$	10.0659	+	6.15462i	0.327790	+	0.200422i
$944$	49.9553	+	29.1298i	1.62591	+	0.948095i
$945$	1.22543			0.0398633
$946$	24.2192	−	71.0954i	0.787434	−	2.31151i
$947$	0.659158	+	0.659158i	0.0214197	+	0.0214197i	0.717736	−	0.696316i	$-0.245179\pi$
$947$	0.659158	+	0.659158i	0.0214197	+	0.0214197i	−0.696316	+	0.717736i	$0.745179\pi$
$948$	−2.15651	−	16.6580i	−0.0700403	−	0.541026i
$949$	−2.92379	−	2.92379i	−0.0949104	−	0.0949104i
$950$	20.6981	+	42.0861i	0.671536	+	1.36545i
$951$	18.0701			0.585964
$952$	5.28116	+	7.95946i	0.171163	+	0.257967i
$953$	−26.8329			−0.869203			−0.434601	−	0.900623i	$-0.643111\pi$
$953$	−26.8329			−0.869203			−0.434601	+	0.900623i	$0.643111\pi$
$954$	7.85183	+	15.9653i	0.254213	+	0.516897i
$955$	−0.933645	+	0.933645i	−0.0302121	+	0.0302121i
$956$	−31.0671	+	40.3071i	−1.00478	+	1.30362i
$957$	−6.77123	−	6.77123i	−0.218883	−	0.218883i
$958$	−18.3089	−	6.23706i	−0.591533	−	0.201510i
$959$		−	19.7443i		−	0.637578i
$960$	−0.316968	+	0.751434i	−0.0102301	+	0.0242524i
$961$	25.6382			0.827037
$962$	1.87039	−	5.49052i	0.0603037	−	0.177021i
$963$	10.6874	−	10.6874i	0.344395	−	0.344395i
$964$	−9.36810	+	12.1544i	−0.301726	+	0.391466i
$965$	−0.589652	+	0.589652i	−0.0189816	+	0.0189816i
$966$	2.00917	−	21.8454i	0.0646439	−	0.702863i
$967$	−15.2802			−0.491379			−0.245690	−	0.969349i	$-0.579014\pi$
$967$	−15.2802			−0.491379			−0.245690	+	0.969349i	$0.579014\pi$
$968$	23.2878	−	15.4516i	0.748497	−	0.496633i
$969$		−	10.2607i		−	0.329620i
$970$	0.418207	+	0.850351i	0.0134278	+	0.0273031i
$971$	−5.62452	−	5.62452i	−0.180499	−	0.180499i	0.611074	−	0.791573i	$-0.290738\pi$
$971$	−5.62452	−	5.62452i	−0.180499	−	0.180499i	−0.791573	+	0.611074i	$0.790738\pi$
$972$	−3.57135	−	27.5869i	−0.114551	−	0.884851i
$973$	17.7153	+	17.7153i	0.567926	+	0.567926i
$974$	−21.3926	−	7.28755i	−0.685462	−	0.233508i
$975$			11.3799i			0.364448i
$976$	26.1708	−	44.8808i	0.837708	−	1.43660i
$977$			15.3837i			0.492169i	0.969248	+	0.246085i	$0.0791441\pi$
$977$			15.3837i			0.492169i	−0.969248	+	0.246085i	$0.920856\pi$
$978$	−8.46334	+	24.8441i	−0.270628	+	0.794427i
$979$	−46.0796	−	46.0796i	−1.47271	−	1.47271i
$980$	−0.0118326	+	0.00153183i	−0.000377979	+	4.89325e-5i
$981$	−4.75382	+	4.75382i	−0.151778	+	0.151778i
$982$	−42.1543	+	20.7317i	−1.34520	+	0.661576i
$983$		−	31.2924i		−	0.998073i	−0.866581	−	0.499037i	$-0.833687\pi$
$983$		−	31.2924i		−	0.998073i	0.866581	−	0.499037i	$-0.166313\pi$
$984$	8.29581	+	1.67807i	0.264461	+	0.0534948i
$985$	1.42513			0.0454084
$986$	1.36560	+	2.77671i	0.0434895	+	0.0884283i
$987$	3.95631	+	3.95631i	0.125931	+	0.125931i
$988$	−15.1954	+	19.7148i	−0.483430	+	0.627211i
$989$	54.1856	−	13.0658i	1.72300	−	0.415468i
$990$	−0.265545	+	0.779508i	−0.00843959	+	0.0247744i
$991$		−	27.6157i		−	0.877241i	−0.898672	−	0.438620i	$-0.855467\pi$
$991$		−	27.6157i		−	0.877241i	0.898672	−	0.438620i	$-0.144533\pi$
$992$	13.0660	+	0.927191i	0.414844	+	0.0294384i
$993$	−15.1991			−0.482329
$994$	−18.2061	+	53.4438i	−0.577461	+	1.69514i
$995$	0.718583	+	0.718583i	0.0227806	+	0.0227806i
$996$	18.9726	+	14.6233i	0.601170	+	0.463358i
$997$	26.4275	+	26.4275i	0.836969	+	0.836969i	0.988459	−	0.151490i	$-0.0484072\pi$
$997$	26.4275	+	26.4275i	0.836969	+	0.836969i	−0.151490	+	0.988459i	$0.548407\pi$
$998$	−22.5070	−	45.7640i	−0.712445	−	1.44863i
$999$			12.0357i			0.380793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.i.b.91.6	yes	80
4.3	odd	2		1472.2.i.b.1103.11		80
16.3	odd	4	inner	368.2.i.b.275.5	yes	80
16.13	even	4		1472.2.i.b.367.12		80
23.22	odd	2	inner	368.2.i.b.91.5	✓	80
92.91	even	2		1472.2.i.b.1103.12		80
368.45	odd	4		1472.2.i.b.367.11		80
368.275	even	4	inner	368.2.i.b.275.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.5	✓	80	23.22	odd	2	inner
368.2.i.b.91.6	yes	80	1.1	even	1	trivial
368.2.i.b.275.5	yes	80	16.3	odd	4	inner
368.2.i.b.275.6	yes	80	368.275	even	4	inner
1472.2.i.b.367.11		80	368.45	odd	4
1472.2.i.b.367.12		80	16.13	even	4
1472.2.i.b.1103.11		80	4.3	odd	2
1472.2.i.b.1103.12		80	92.91	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33867 - 0.456028i) q^{2} +(0.860099 + 0.860099i) q^{3} +(1.58408 + 1.22094i) q^{4} +(0.0592628 - 0.0592628i) q^{5} +(-0.759160 - 1.54362i) q^{6} +2.65917i q^{7} +(-1.56377 - 2.35682i) q^{8} -1.52046i q^{9} +(-0.106359 + 0.0523078i) q^{10} +(3.23118 + 3.23118i) q^{11} +(0.312330 + 2.41260i) q^{12} +(1.32495 - 1.32495i) q^{13} +(1.21266 - 3.55975i) q^{14} +0.101944 q^{15} +(1.01859 + 3.86813i) q^{16} +1.27002i q^{17} +(-0.693372 + 2.03539i) q^{18} +(-4.69664 + 4.69664i) q^{19} +(0.166233 - 0.0215203i) q^{20} +(-2.28715 + 2.28715i) q^{21} +(-2.85197 - 5.79899i) q^{22} +(2.50175 - 4.09161i) q^{23} +(0.682105 - 3.37210i) q^{24} +4.99298i q^{25} +(-2.37788 + 1.16946i) q^{26} +(3.88804 - 3.88804i) q^{27} +(-3.24670 + 4.21233i) q^{28} +(-1.21823 + 1.21823i) q^{29} +(-0.136469 - 0.0464892i) q^{30} +2.31556i q^{31} +(0.400417 - 5.64266i) q^{32} +5.55826i q^{33} +(0.579165 - 1.70014i) q^{34} +(0.157590 + 0.157590i) q^{35} +(1.85639 - 2.40852i) q^{36} +(-1.54778 + 1.54778i) q^{37} +(8.42905 - 4.14545i) q^{38} +2.27918 q^{39} +(-0.232345 - 0.0469985i) q^{40} +2.46013i q^{41} +(4.10474 - 2.01873i) q^{42} +(8.21821 + 8.21821i) q^{43} +(1.17335 + 9.06351i) q^{44} +(-0.0901066 - 0.0901066i) q^{45} +(-5.21491 + 4.33645i) q^{46} -1.72980i q^{47} +(-2.45089 + 4.20307i) q^{48} -0.0711808 q^{49} +(2.27694 - 6.68395i) q^{50} +(-1.09234 + 1.09234i) q^{51} +(3.71651 - 0.481132i) q^{52} +(5.85076 - 5.85076i) q^{53} +(-6.97787 + 3.43175i) q^{54} +0.382977 q^{55} +(6.26719 - 4.15833i) q^{56} -8.07915 q^{57} +(2.18635 - 1.07526i) q^{58} +(10.2226 - 10.2226i) q^{59} +(0.161487 + 0.124468i) q^{60} +(-9.18423 - 9.18423i) q^{61} +(1.05596 - 3.09978i) q^{62} +4.04316 q^{63} +(-3.10924 + 7.37107i) q^{64} -0.157040i q^{65} +(2.53473 - 7.44068i) q^{66} +(0.241049 - 0.241049i) q^{67} +(-1.55062 + 2.01181i) q^{68} +(5.67094 - 1.36744i) q^{69} +(-0.139095 - 0.282826i) q^{70} -15.0134 q^{71} +(-3.58345 + 2.37765i) q^{72} -2.20672i q^{73} +(2.77781 - 1.36614i) q^{74} +(-4.29446 + 4.29446i) q^{75} +(-13.1742 + 1.70550i) q^{76} +(-8.59224 + 8.59224i) q^{77} +(-3.05107 - 1.03937i) q^{78} -6.90459 q^{79} +(0.289601 + 0.168872i) q^{80} +2.12683 q^{81} +(1.12189 - 3.29330i) q^{82} +(6.96262 - 6.96262i) q^{83} +(-6.41550 + 0.830539i) q^{84} +(0.0752648 + 0.0752648i) q^{85} +(-7.25373 - 14.7492i) q^{86} -2.09559 q^{87} +(2.56250 - 12.6681i) q^{88} -14.2609 q^{89} +(0.0795318 + 0.161714i) q^{90} +(3.52326 + 3.52326i) q^{91} +(8.95858 - 3.42693i) q^{92} +(-1.99162 + 1.99162i) q^{93} +(-0.788838 + 2.31563i) q^{94} +0.556672i q^{95} +(5.19765 - 4.50885i) q^{96} -7.99512i q^{97} +(0.0952876 + 0.0324605i) q^{98} +(4.91287 - 4.91287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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